Question

A boundary stripe 6 in. wide is painted around a rectangle whose dimensions are 120 ft by 230 ft. Use differentials to approximate the number of square feet of paint in the stripe.

Answer 1

Answer:

350 square feet

Step-by-step explanation:

We are given that

Width of strip=6 in

Dimension of rectangle=$20 ft\times 230 ft$

We know that

Area  of rectangle ,A=xy

Differentiate

$dA=\frac{\partial A}{\partial x}x+\frac{\partial A}{\partial y}y$

We have $\frac{\partial A}{\partial x}=y=230 ft$

$\frac{\partial A}{\partial y}=x=120$

$dx=\frac{12}{12}=1 ft$

1 ft=12 in

Because 6 in added in both side of breadth

dy=$\frac{12}{12}=1 ft$

Because 6 in added on both sides of length of rectangle

Substitute the values

$dA=230\times 1+120\times 1=350 ft^2$

Hence, the number of square feet of paint in the strip=350 square feet