Question

The diagonals of a square and that of a rectangle with length 12cm and breadth 8cm are equal. Find the side of the square correct to two decimal places.

Answer 1

dimensions of rect ,

l = 12cm , b = 8cm

now by applying Pythagoras, we can find its diagonal(D) , since all angles are of 90°

now,

.

$d = \sqrt{ {12}^{2} + {8}^{2} } \: cm$

$d = \sqrt{208} \: cm = 14.42cm \: (approx)$

since diagonal of square nd rect is equal then ,

for square, let its side be 'S'

d = √(S^2 + S^2) {all sides of square are equal

therefore ,

$d = \sqrt{ {s}^{2} + {s}^{2} }$

$14.42 = \sqrt{2 {s}^{2} } \: = \: s \sqrt{2}$

$= > \: s = 14.42 \div \sqrt{2} = 14.42 \sqrt{2} \div 2$

$final \: answer = \: 7.21 \sqrt{2} \: cm$

HOPE it WILL HELP YOU..

THNKS!