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Question

The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when the side is 10 cm, is _____________.


Solution


Let x be the side and A be the area of an equilateral triangle at any time t.

It is given that, 

dxdt = 2 cm/sec

Area of the equilateral triangle, A34Side2 = 34x2                  

A=34x2

Differentiating both sides with respect to t, we get

dAdt=34×ddtx2

dAdt=34×2xdxdt

dAdt=32xdxdt

When x = 10 cm and dxdt = 2 cm/sec, we get

dAdt=32×10×2

dAdt=103 cm2/sec

Thus, the area of the equilateral triangle increases at the rate of 103 cm2/sec.


The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when the side is 10 cm, is       103 cm2/sec      .

Mathematics
RD Sharma XII Vol 1 (2019)
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