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? estimate the length and width of the rectangle. how can you estimate the side length of each square? a. estimate $sqrt{48}$ b. estimate $sqrt{96}$ c. estimate $sqrt{96}div4$ d. estimate $sqrt{48}div4$

Explanation:

Step1: Recall perfect - square numbers

Find the perfect - square numbers closest to 48 and 96. For 48, $6^2 = 36$ and $7^2=49$. For 96, $9^2 = 81$ and $10^2 = 100$.

Step2: Estimate $\sqrt{48}$

Since 48 is closer to 49 than 36, $\sqrt{48}\approx7$.

Step3: Estimate $\sqrt{96}$

Since 96 is closer to 100 than 81, $\sqrt{96}\approx10$.

Step4: Analyze $\frac{\sqrt{48}}{4}$

$\frac{\sqrt{48}}{4}\approx\frac{7}{4}=1.75$.

Step5: Analyze $\frac{\sqrt{96}}{4}$

$\frac{\sqrt{96}}{4}\approx\frac{10}{4} = 2.5$.

Answer:

A. Estimate $\frac{\sqrt{48}}{4}\approx1.75$
B. Estimate $\frac{\sqrt{96}}{4}\approx2.5$
C. Estimate $\sqrt{96}\approx10$
D. Estimate $\sqrt{48}\approx7$