Question

Recall the formula for finding the area of a rectangle. Define a

variable for the width and set up an equation to find the dimensions of a
rectangle that has an area 144 square inches, given that the length is 10
inches longer than its width.

Answer 1

w=width,
w(w+10)=144
______
The formula for a rectangle area is length times width.

Answer 2

`x^2+10x=144`

Explanation:

Given : The length is 10 inches longer than its width.

Area of rectangle is 144 sq.inches

To Find : Define a variable for the width and set up an equation to find the dimensions of a rectangle

Solution:

Let the width be x

Since we are given that The length is 10 inches longer than its width.

So, Length of rectangle = x+10

Area of rectangle =
`Length * Width`

=
`x * (x+10)`

We are given that Area of rectangle is 144 sq.inches

So,
`x * (x+10) =144`

`x^2+10x=144`

`x^2+18x-8x-144=0`

`x(x+18)-8(x+18)=0`

`(x+18)(x-8)=0`

`x=-18,8`

Since width cannot be negative

So, width of rectangle is 8 inches

Length of rectangle = x+10 = 8+10 = 18

Hence an equation to find the dimensions of a rectangle that has an area 144 square inches is
`x^2+10x=144`