Question

think about the process the length of a rectangle is twice the width. the area of the rectangle is 96 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? how can you estimate the side length of each square? a. estimate $sqrt4{48}$ b. estimate $\frac{sqrt{96}}{4}$ c. estimate $sqrt{96}$ d. estimate $sqrt{48}$. the rectangle is $square$ units long and $square$ units wide. (round to the nearest tenth as needed.)

Explanation:

Step1: Let the width of the rectangle be $x$ units.

Since the length of the rectangle is twice the width, the length is $2x$ units.

Step2: Use the area formula for a rectangle.

The area of a rectangle $A = \text{length}\times\text{width}$. Given $A = 96$ square - units, so $2x\times x=96$, which simplifies to $2x^{2}=96$. Then $x^{2}=48$, and $x = \sqrt{48}$.

Step3: Find the length.

The length is $2x$, so the length is $2\sqrt{48}$.

Step4: Estimate $\sqrt{48}$.

We know that $6^{2}=36$ and $7^{2}=49$. Since $48$ is closer to $49$, $\sqrt{48}\approx6.9$.

Step5: Find the length and width of the rectangle.

The width $x\approx6.9$ units, and the length $2x\approx2\times6.9 = 13.8$ units.

Answer:

The rectangle is $13.8$ units long and $6.9$ units wide.