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.In your final answer, include your diagram, and all formulas, equations, and calculations necessary to solve for the length of Kamila’s bedroom.

Answer 1

The length of each side of Kamila’s square bedroom is;

`9\text{ feet}`

For the Living room;

`\begin{gathered} A_l=18*1.25x \\ A_l=22.5x\text{ --------1} \end{gathered}`

For the bedroom;

`\begin{gathered} A_b=x* x \\ A_b=x^2\text{ -----------2} \end{gathered}`

Recall that the area of Kamila’s rectangular living room is 2.5 times the area of her square bedroom;

`A_l=2.5A_b\text{ ----------3}`

Step-by-step explanation:

Given that 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.

Recall that the area of a rectangle can be calculated using the formula;

`A=l* b`

For the Living room;

`\begin{gathered} A_l=18*1.25x \\ A_l=22.5x\text{ --------1} \end{gathered}`

For the bedroom;

`\begin{gathered} A_b=x* x \\ A_b=x^2\text{ -----------2} \end{gathered}`

Recall that the area of Kamila’s rectangular living room is 2.5 times the area of her square bedroom;

`A_l=2.5A_b\text{ ----------3}`

substituting equations 1 and 2 into equation 3;

`\begin{gathered} A_l=2.5A_b\text{ ----------3} \\ 22.5x=2.5(x^2) \\ x=(22.5)/(2.5) \\ x^{}=9 \\ x=9\text{ feet} \end{gathered}`

Therefore, the length of each side of the square bedroom is;

`9\text{ feet}`