Question

if the perimeter of rectangle is p unit and diagonal is d unit then difference between length and breadth of rectangle is

Answer 1

Difference between the length and breath =
let suppose length =x cm
.....................breadth = y cm
= x-y cm

Answer 2

perimeter of rectangle = 2( l+b ) = p

so , l+b = p/2

and diagonal of rectangle = ( l² + b²)^½ = d

so, l² + b² = d²

now ,

( l+b )² = l² + b² + 2lb

p² = d² + 2lb

=> lb = (p²-d²)/2

now ,

( l+ b)² = ( l - b)² + 4lb

(l - b)² = p² - 4 (p²-d²)/2

(l - b)² = p² - 2p² + 2d²

(l - b)² = 2d² - p²

l - b = ( 2d² - p² )^½