Question

10) Gabe put up a fence around his rectangular vegetable garden this weekend.

Answer 1

Answer:

The length is 16 ft, and the width is 3 ft.

Step-by-step explanation:

Let L = length & let W = width.

The perimeter of a rectangle is

P = 2(L + W)

The area of a rectangle is

A = LW

We know the perimeter and the area, so we substitute those values int he equations above and we switch sides in both equations.

Perimeter: 2(L + W) = 38

Divide both sides by 2:

L + W = 19

Area: LW = 48

We have a system of two equations in two unknowns:

L + W = 19

LW = 48

Solve the first equation for L and substitute it into the second equation.

L = 19 - W

(19 - W)W = 48

19W - W^2 - 48 = 0

Multiply both sides by -1, and rearrange the order of the terms.

W^2 - 19W + 48 = 0

(W - 16)(W - 3) = 0

W - 16 = 0 or W - 3 = 0

W = 16 or W = 3

Use W = 3 to find L

L = 19 - W

L = 19 - 3

L = 16

Answer: The length is 16 ft, and the width is 3 ft.