Q19 of 99 Page 264

If the length of diagonal of a rectangle is 10 cm. and area is 62.5 sq. cm., then the sum of their length and breadth is

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

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