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I`d a square and rectangle has same perimeter and their areas are A1 and A2. Then equality if A1 and A2 is A) A1>A2 B) A1>_A2 C) A1

I`d a square and rectangle has same perimeter and their areas are A1 and A2. Then equality if A1 and A2 is A) A1>A2 B) A1>_A2 C) A1

Grade:12

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
8 years ago
let the side of square be a
and rectangle be of length l and width w
perimiter equal gives
4a = 2(l+w)
a = (l+w)/2
Now A1 = a2
A2 = lw
Then by AM>GM
A1 = a^2 = (l+w)^2/4 \geq lw = A2
hence Option C

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