#### To determine

**To find:** The rate of change of the area of an equilateral triangle.

#### Answer

The rate of change of the area of an equilateral triangle is dAdt=1505 cm2/min.

#### Explanation

**Given:**

The rate of change of sides of an equilateral triangle is 10 cm/min.

**Formula used:**

(1) Chain rule: dydx=dydu⋅dudx

(2). Area of an equilateral triangle of sides a:A=34a2 .

**Calculation:**

Let A be the area of the equilateral triangle and a be the length of each sides.

Since sides of the equilateral triangle are changes with time t. Therefore, area of the triangle become also changes with time t .

This means that area and sides of the triangle are function of the time t .

Since dadt=10 cm/min .

Obtain dAdt when a=30 cm .

Differentiate A with respect to the time t .

ddt[A]=ddt[34a2]dAdt=34dda[a2]dadt [Qdydx=dydu⋅dudx]=34(2a)dadt=(32a)dadt

Substitutes a=30 and dadt=10 in dAdt .

dAdt=32×30×10=30032=1503 cm2/min

Therefore, the rate of change of the area of an equilateral triangle is dAdt=1505 cm2/min.