Question

think about the process the length of a rectangle is twice the width. the area of the rectangle is 90 square units. notice that you can divide the rectangle into two squares with equal area. how can you estimate the side length of each square? estimate the length and width of the rectangle.

how can you estimate the side length of each square?

a. estimate \\(\sqrt{45}\\).

b. estimate \\(\frac{\sqrt{90}}{4}\\).

c. estimate \\(\frac{\sqrt{45}}{4}\\).

d. estimate \\(\sqrt{90}\\).

the rectangle is \\(\square\\) units long and \\(\square\\) units wide.
(round to the nearest tenth as needed.)

Explanation:

Step1: Find area of one square

The rectangle area is 90, so each square has area $\frac{90}{2}=45$.

Step2: Relate square area to side length

Square area = $s^2$, so side $s=\sqrt{45}$. This confirms option A.

Step3: Define rectangle variables

Let width = $w$, length = $2w$.

Step4: Set up rectangle area equation

Area: $w \times 2w = 90$ → $2w^2=90$

Step5: Solve for width $w$

$w^2=45$ → $w=\sqrt{45}\approx6.7$

Step6: Calculate rectangle length

Length = $2w=2\times6.7=13.4$

Answer:

A. Estimate $\sqrt{45}$.
13.4 units long and 6.7 units wide.