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The base of the triangle is decreasing at the rate of 1.6 cm/min.
Given
dh/dt = 1 cm/min
dA/dt = 2 cm2/min
When A = 100 cm2, h = 10 cm
We know that
A = 1/2 × b × h
b = 20 cm
Let us differentiate both sides
dA/dt = 1/2 [b dh/dt + h db/dt]
Substituting the values
2 = 1/2 [20 × 1 + 10 × db/dt]
By further simplification
4 = 20 + 10 db/dt
db/dt = -1.6 cm/min
Therefore, the base of the triangle is decreasing at the rate of 1.6 cm/min.
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