Worksheet Perimeter of Triangles

Perimeter of Triangles Website Worksheet

Q. No. 1

Sita has a triangular vegetable patch in her backyard with side measurements of $12\text{ m}$, $16\text{ m}$, and $20\text{ m}$. She wants to put a wire fence around it to protect her tomatoes from stray chickens.

a) Write the formula to find the perimeter of a triangle having sides a, b, and c. [1K]
b) If Sita changes her mind and decides to make the patch a perfect equilateral triangle where each side is $15\text{ m}$, explain how the perimeter calculation changes and find its new perimeter. [1U]
c) If she goes with her original backyard patch ($12\text{ m}$, $16\text{ m}$, $20\text{ m}$) and decides to fence it 4 times, find the total cost of the wire at the rate of $\text{Rs. } 35/\text{m}$. [2A]
d) Sita finds a leftover piece of wire in her shed that is exactly $250\text{ m}$ long. Will this wire be enough to fence her original patch 5 times? Justify your answer. [1HA]

Q. No. 2

Pasang is running a single-strand decorative light wire around a traditional triangular frame for a local festival in Manang. The three sides of the wooden frame measure $25\text{ cm}$, $30\text{ cm}$, and $35\text{ cm}$.

a) State the variable in the formula L = nP that represents the number of rounds the wire goes around the perimeter. [1K]
b) If Pasang cuts the frame exactly in half along its symmetrical axis, what happens to the perimeter of the resulting shapes? Describe using the property of sides. [1U]
c) Find the total cost of the decorative light wire to go around the frame 3 times if the merchant charges $\text{Rs. } 5/\text{cm}$. [2A]
d) A vendor offers Pasang a pre-packaged roll of lights measuring $500\text{ cm}$ and says it will easily wrap around the frame 6 times. Is the vendor correct? Justify your calculation. [1HA]

Q. No. 3

Bikram is building a triangular wooden table top for a cafe in Bhaktapur. The sides of the table are designed to be in the strict proportion of 3:4:5.

a) Write down an algebraic expression for the perimeter (P) of this triangle using a common multiplier x. [1K]
b) If the shortest side of this table must be exactly $60\text{ cm}$ to fit into a corner, deduce the values of the remaining two sides. [1U]
c) Using the dimensions from part (b), find the cost of a rubber protective strip to wrap around the table edge exactly 2 times at the rate of $\text{Rs. }$ $2/\text{cm}$. [2A]
d) Bikram has a budget of exactly $\text{Rs. }$ 1,000 for the rubber strips. Can he afford to wrap the table edge 3 times if the rate stays the same? Justify your response. [1HA]

Q. No. 4

Anil sir is setting up a triangular running track for young students at a primary school in Pokhara. The dimensions of the track sides are $35\text{ m}$, $45\text{ m}$, and $50\text{ m}$.

a) Define the mathematical term "perimeter" in the context of this running track. [1K]
b) If a student runs one full lap, they cover the standard perimeter. If they run a second lap but skip the shortest side by cutting straight across, will their total distance increase or decrease? Explain. [1U]
c) Anil sir wants to mark the boundary line using white chalk powder 3 times. Find the total cost of the chalk needed if it costs $\text{Rs. } 15/\text{m}$ to lay down a single line. [2A]
d) The school sports department provides a budget that covers exactly $700\text{ m}$ worth of chalk line marking. Is this budget sufficient to complete a $5\text{-time}$ marking of the track? Justify your answer. [1HA]

Q. No. 5

Maya is weaving a triangular Dhaka pattern on her loom. The pattern features an isosceles triangle where the two equal slanting sides measure $18\text{ cm}$ each, and the flat baseline measures $14\text{ cm}$.

a) Write down the specific formula for the perimeter of an isosceles triangle with equal sides a and base b. [1K]
b) If Maya decides to stretch the baseline so that it becomes equal to the other two sides, what special type of triangle is formed, and what will its new perimeter be? [1U]
c) She needs to stitch a golden thread along the border of the original pattern 5 times. Find the cost of the golden thread at the rate of $\text{Rs. } 4/\text{cm}$. [2A]
d) Maya bought a spool of golden thread containing $1,200\text{ cm}$. Can she complete this 5-time border stitch on 5 identical triangular patterns using only this spool? Justify mathematically. [1HA]

Q. No. 6

Kiran has a large triangular field in Chitwan used for goat grazing. The sides of the field measure $80\text{ m}$, $90\text{ m}$, and $110\text{ m}$. He wants to install an electric fence to keep wild animals out.

a) Write down the formula that links Total Cost (TC), Rate (R), and Total Length of wire (L). [1K]
b) If Kiran changes the shape of the field but keeps the total length of the boundary exactly the same, does the perimeter change? Explain why or why not. [1U]
c) Find the cost of the fencing wire if he runs the wire 3 times around the field at the rate of $\text{Rs. } 55/\text{m}$. [2A]
d) A cooperative agent offers him a bulk package of wire measuring $1,500\text{ m}$ to fence the field 5 times. Will Kiran have enough wire, or will he fall short? Justify your answer with exact figures. [1HA]

Q. No. 7

Sunita is designing a triangular display sign for her shop in Lalitpur. The dimensions of the metal frame sides are $50\text{ cm}$, $60\text{ cm}$, and $70\text{ cm}$.

a) What is the total perimeter (P) of the display sign frame? [1K]
b) If Sunita wants to scale down the display sign to exactly half its current size for a smaller window, what will be the new length of each side? [1U]
c) She wants to protect the edge of the original large frame ($50\text{ cm}$, $60\text{ cm}$, $70\text{ cm}$) by winding a colored tape 4 times around it. Find the cost of the tape if it costs $\text{Rs. } 1.50/\text{cm}$. [2A]
d) If she has $1,000\text{ cm}$ of colored tape, can she complete the 4-time wrapping on the large frame and still have enough tape left over to wrap the smaller scaled-down frame (from part b) exactly 2 times? Justify. [1HA]

Q. No. 8

Rajesh is constructing a triangular brick border around a flower bed in a public park. The three side lengths are $15\text{ m}$, $20\text{ m}$, and $25\text{ m}$.

a) Write the formula for finding the total length of materials needed (L) when making n rounds of a perimeter P. [1K]
b) If the flower bed was shaped as a square with the exact same perimeter as this triangle, what would be the length of one side of that square bed? [1U]
c) Rajesh decides to lay a steel reinforcement cable 3 times along the brick border before finalizing it. Find the cost of this cable at the rate of $\text{Rs. } 85/\text{m}$. [2A]
d) The contractor hands Rajesh a single cable line measuring $500\text{ m}$. Is this line long enough to circle the flower bed 8 times? Justify your mathematical reasoning. [1HA]

Q. No. 9

Dolma operates a yak farm in Mustang with a triangular layout. The boundary parameters measure $60\text{ m}$, $75\text{ m}$, and $85\text{ m}$.

a) If all three sides of a triangle are completely different in length, what is the specific classification name of this triangle? [1K]
b) If Dolma expands the pasture by adding exactly $5\text{ m}$ to every single side, how much will the total perimeter increase? Explain the structural arithmetic. [1U]
c) She chooses to install a heavy barbwire fence running 4 times around the original pasture ($60\text{ m}$, $75\text{ m}$, $85\text{ m}$). Find the total cost of the wire if the market rate is $\text{Rs. } 120/\text{m}$. [2A]
d) Dolma has a budget of $\text{Rs. } 100,000$ specifically for fencing. Will this budget allow her to fence the original pasture 5 times at the same rate? Justify your calculation. [1HA]

Q. No. 10

Niranjan is making a scale model of a historical triangular fort. The blueprints (design) indicate the physical prototype (sample) sides are $40\text{ m}$, $50\text{ m}$, and $70\text{ m}$.

a) Write down the formula for calculating Total Cost when Rate and Length are given. [1K]
b) If the model fort is an exact scale match but its perimeter is exactly $10\text{ times}$ smaller than the prototype, what is the perimeter of the model? [1U]
c) Niranjan needs to put a security wire around the prototype fort ($40\text{ m}$, $50\text{ m}$, $70\text{ m}$) exactly 3 times. Find the total cost of the wire at the rate of $\text{Rs. } 45/\text{m}$. [2A]
d) If the security team buys a standard industrial wire roll of $1,000\text{ m}$, will it be enough to fence the prototype fort 6 times? Justify your answer. [1HA]