Question

A wire when bent in the form of a square encloses an area of 900 cm². Find the largest area enclosed by the same wire when bent to form an equilateral triangle.

Answer 1

Given: A wire bent in the form of a square encloses area = 900 cm². Find the largest area enclosed by the same wire when bent to form an equilateral triangle.

Step-wise calculation:

1. Let side of the square = s.

Then s² = 900

⇒ s = `sqrt(900)`

= 30 cm

2. Length of the wire perimeter of square = 4s

= 4 × 30

= 120 cm

3. If bent into an equilateral triangle, each side

a = `120/3`

= 40 cm

4. Area of an equilateral triangle of side a is `(sqrt(3)/4) a^2`. 

So, Area = `(sqrt(3)/4) xx (40)^2` 

= `(sqrt(3)/4) xx 1600`

= `400sqrt(3)` cm² 

Numerical approx:

`400sqrt(3)`

= 400 × 1.732 

= 692.82 cm² 

The largest area enclosed when the same wire is bent to form an equilateral triangle is `400sqrt(3)` cm² (≈ 692.82 cm²).