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The diagonal of a square is increasing at 0.5 cm/s. When the area of the square is 400 cm², what is the rate at which its area is changing?

1. 20√2 cm²/s
2. 10√2 cm²/s
3. 1/(10√2) cm²/s
4. 10/√2 cm²/s

Correct answer: 10√2 cm²/s

Solution

Area A=d^2/2, so dA/dt=d*(dd/dt). When A=400, side=20 and diagonal d=20*sqrt(2). Thus dA/dt=20*sqrt(2)*0.5=10*sqrt(2) cm^2/s.

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