Question

The area of Kamila’s rectangular living room is 2.5 times the area of her square bedroom. The length of the living room is 18 feet and its width is 1.25 times the length of a side of the bedroom.

Create a diagram representing Kamila’s living room and her square bedroom. Assign variables to any unknown sides and label the diagram.
Find the length of one side of Kamila’s bedroom.

Answer 1

The length of one side of Kamila’s bedroom is 9 feet.

Explanation:

Let the side of square room be x

Length of rectangular room = 18 feet.

Since we are given that its width is 1.25 times the length of a side of the bedroom.

So, width = 1.25 x

Area of rectangular room =
`Length * Width`

=
`18 * 1.25x`

=
`22.5x`

Area of square bedroom =
`Side^2`

=
`x^2`

Since we are given that The area of Kamila’s rectangular living room is 2.5 times the area of her square bedroom.

So,
`22.5x = 2.5x^2`

`22.5 = 2.5x`

`(22.5)/(2.5)=x`

`9=x`

Thus the length of one side of Kamila’s bedroom is 9 feet.

Width of rectangular living room = 1.25x =
`1.25 * 9 =11.25 feet`

Refer the attached diagram

Answer 2

Let L be the length of one side of Kamila's bedroom (since her bedroom is square, the area would be L x L). Then the width of her living room is 1.25L. So:
18*1.25L=2.5(L)²
22.5L=2.5L²
L=22.5/2.5=9
Kamila's bedroom is 9'x9'; her living room is 11.25'x18'. ☺☺☺☺