Question

A lawn is in the form of an isosceles triangle. The cost of turfing on it came to $₹ 1{,}200$ at ₹ 4 per m$^2$. If the base be 40 m long, find the length of each side.

• A. 25 m
• B. 24 m
• C. 26 m
• D. None of these

Hint:

For isosceles triangles, drop the altitude to split the base equally, then apply Pythagoras with the half-base.

Answer 1

The Correct Option is A

Step 1: Compute area from cost. 
$Rate = ₹ 4 \text{ per m$^2$}, Cost = ₹ 1200$ $\Rightarrow$ $\text{Area} = \dfrac{1200}{4} = 300\ \text{m}^2.$ 
Step 2: Let equal sides be \(x\). $\text{ Base } = 40\ \text{m}.$ 
In an isosceles triangle, altitude to base bisects it: each half = 20 m. 
Height \(h = \sqrt{x^2 - 20^2} = \sqrt{x^2 - 400}\). 
Step 3: Use area formula. 
\(\dfrac{1}{2}\times 40 \times h = 300 \Rightarrow 20\sqrt{x^2-400}=300 \Rightarrow \sqrt{x^2-400}=15\). 
\(\Rightarrow x^2 - 400 = 225 \Rightarrow x^2 = 625 \Rightarrow x = 25\ \text{m}\). 
Step 4: Conclude. 
Each equal side \(= \boxed{25\ \text{m}}\).