The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 7 cm/s. When the length is 11 cm and the width is 7 cm, how fast is the area of the rectangle increasing?

Question

Ariella

Physics

10 October, 11:40

The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 7 cm/s. When the length is 11 cm and the width is 7 cm, how fast is the area of the rectangle increasing?

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Answers (1)

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Aryan Brooks · Answer 1

dA/dt = 140 cm²/s

Explanation:

The length of a rectangle is increasing at the rate of 9 cm/s. This means rate at which the length is changing with time = 9 cm/s

dL/dt = 9 cm/s

The width is increasing at the rate of 7 cm/s.

dW/dt = 7 cm/s

When the length is 11 cm and the width is 7 cm, How fast is the area of the rectangle increasing?

Area of a rectangle = Length * width

Area of a rectangle = Lw

we need the product rule to find the rate the area of the rectangle is changing.

dA/dt = LdW/dt + W dL/dt

dA/dt = 11 (7) + 7 (9)

dA/dt = 77 + 63

dA/dt = 140 cm²/s