Question

the altitude (i.e., height) of a triangle is increasing at a rate of 1.5 cm/minute while the area of the triangle is increasing at a rate of 3.5 square cm/minute. at what rate is the base of the triangle changing when the altitude is 11.5 centimeters and the area is 94 square centimeters?

Answer 1

Change in base of right angled triangle is - 1.5cm/minute

What is rate of change in area?

The rate of change in area is defined as the change in with respect to time.

dA/dt = 1/2(BdH/dt + HdB/dt)

where A is area, B is base, H is height

According to given data:

A = 1/2×B×H

94 = 1/2×11.5×B

⇒ B = 94×2/11.5 = 16.3cm

Rate of change in base,

dA/dt = 1/2(BdH/dt + HdB/dt)

3.5 = 1/2(16.3×1.5 + 11.5×dB/dt)

dB/dt = 7-24.45/11.5 = -1.5 cm/minute

Thus,base of triangle is decreasing by 1.5cm/minute.

To know more about right angled triangle visit:

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