Question

A wire when bent in the form of a square encloses an area of 225 cm². Find the largest area enclosed by the same wire when bent to form a rectangle of breadth 12 cm.

Answer 1

Given: A wire bent as a square encloses area 225 cm²; the same wire is bent to form a rectangle whose breadth is 12 cm.

Step-wise calculation:

1. Side of the square = `sqrt(225)` = 15 cm.

2. Perimeter of the square (length of the wire) = 4 × 15 = 60 cm.

3. For the rectangle with breadth b = 12 cm and length l, perimeter = 2(l + b) = 60.

So, l + 12 = 30 ⇒ l = 18 cm.

4. Area of the rectangle = l × b

= 18 × 12

= 216 cm²

The largest area enclosed by the same wire when bent to form a rectangle of breadth 12 cm is 216 cm².