Question

A wire when bent in the form of a square encloses an area = 576 cm². Find the largest area enclosed by the same wire when bent to form;
(i) an equilateral triangle.
(ii) A rectangle whose adjacent sides differ by 4 cm.

Answer 1

Let a be the length of each side.
a² = 576
a = 24 cm
4a = 96 cm
Hence length of the wire = 96 cm

(i) For the equilateral triangle,
side = `96/3` = 32 cm

Area = `sqrt3/4`( side )²

        = `sqrt3/4` x 32²

        = 256√3 sq.cm

(ii) Let the adjacent side of the rectangle be x and y cm.
Since the perimeter is 96 cm, we have,
2( x + y ) = 96
Hence,
x + y = 48
x - y = 4
x = 26
y = 22
Hence area of the rectangle is = 26 x 22 = 572 sq.cm