Question

The blueprint of a rectangular fountain shows that the length will be 7 feet longer than twice it's width. The area of the rectangular fountain is 85 feet​ squared.

Part A
Which equation represents the area of the fountain?

A
(w)(w+7) = 85
B
(w)(2w−7)=85
C
(w+7)(2w)=85
D
(w)(2x+7)=85

Answer 1

The equation that represents the area is (7 + 2W)(W) = 85

Explanation:

Given

Length = 7 ft longer than twice its Width

Area = 85 ft²

Required

Expression for area of the fountain

Let L represent the length of the fountain

Let W represent the width of the fountain

and

Let A represent the area of the fountain

The expected length is said to be 7 ft longer than twice its Width

We'll break this statement into bits and represent it mathematically, as follows:

twice its Width means 2 * W

7 ft longer than means 7 +

Combining these together; it gives

= 7 + 2 * W

= 7 + 2W

Hence,

L = 7 + 2W

Recall that the area of a rectangle is calculated using the following formula

Area = Length * Width

This formula is represented mathematically as follows:

A = L * W

By substituting 85 for A and 7 + 2W for L, we have

85 = (7 + 2W) * W

85 = (7 + 2W)(W)

Re order

(7 + 2W)(W) = 85

Hence, the equation that represents the area is (7 + 2W)(W) = 85