Question

The length of a rectangle is 7 inches longer than it is wide. If the area is 20 square inches, what are the dimensions of the rectangle?

Answer 1

Explanation:

Step 1: Find the dimensions

l = 7 + w

Area = 20

Find width

`A = l * w`

`20 = (7 + w)(w)`

`20 - 20 = 7w + w^2 - 20`

`w^2 + 7w - 20 = 0`

`w=(-(7)\pm√((7)^2-5(1)(-20)))/(2(1))`

`w = 2.17890...`

Find length

`l = 7 + w`

`l = 7 + 2.17890...`

`l = 9.17890...`

Answer:
`Width = 2.17890..., Length = 9.17890...`

Answer 2

Area of a rectangle is length x width.

Let the width = x

The length would be x +7. ( 7 inches longer than the width)

Area = 20

Set up the formula:

20 = x * x+7

Simplify the right side:

20 = x^2 + 7x

Subtract 29 from both sides:

X^2 + 7x -20 = 0

Solve using the quadratic equation

X = -b + sqrt(b^2 -4ac) / 2a

X = -7 + sqrt(7^2-4(1)(-20) / 2(1) (exact answer)

X = 2.178908 ( as a decimal)

The width is 2.178907 inches (round as needed)

The length would be 9.178907 inches ( round as needed.)

Depending on how you round, when you multiply them together you get approximately 20 square inches.