Question

think about the process the length of a rectangle is twice the width. the area of the rectangle is 66 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 $\frac{sqrt{33}}{4}$ b. estimate $sqrt{33}$. c. estimate $sqrt{66}$. d. estimate $\frac{sqrt{66}}{4}$. the rectangle is units long and units wide. (round to the nearest tenth as needed.)

Explanation:

Step1: Find area of each square

Since the rectangle of area 66 square - units is divided into two equal - area squares, the area of each square is $\frac{66}{2}=33$ square units.

Step2: Recall the formula for the area of a square

The area of a square is $A = s^{2}$, where $s$ is the side - length of the square. If $A = 33$, then $s=\sqrt{33}$. So, to estimate the side - length of each square, we estimate $\sqrt{33}$.

Step3: Estimate the length and width of the rectangle

The width of the rectangle is equal to the side - length of the square, $w=\sqrt{33}\approx5.7$ (since $5.7^{2}=32.49$). The length of the rectangle is twice the width, $l = 2\sqrt{33}\approx11.5$ (since $2\times5.7 = 11.4$).

Answer:

B. Estimate $\sqrt{33}$
The rectangle is 11.5 units long and 5.7 units wide.