If the length of

Let sides of rectangle be L and B.

We know, Diagonal =

Or Diagonal² = L² + B²

⇒ 10² = L² + B²

⇒ 100 sq. cm = L² + B²

This can be rewritten as

100 = (L + B)² – 2LB

Area of rectangle = L × B = 62.5 sqcm

Hence,

100 = (L + B)² - 2 × 62.5

⇒ (L + B)² = 100 + 125

Or L + B = = 15cm