Question

think about the process
the length of a rectangle is twice the width. the area of the rectangle is 74 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 (\frac{sqrt{74}}{4})
b. estimate (\frac{sqrt{37}}{4})
c. estimate (sqrt{74})
d. estimate (sqrt{37})

Explanation:

The rectangle's area is 74, and it's divided into two equal - area squares. So the area of each square is $\frac{74}{2}=37$. The side length of a square is the square root of its area, so we need to estimate $\sqrt{37}$. Option B is to estimate $\frac{\sqrt{37}}{4}$ which is incorrect. Option A is $\frac{\sqrt{74}}{4}$, wrong. Option C is $\sqrt{74}$, wrong. Option D is to estimate $\sqrt{37}$, which is correct as the area of each square is 37.

Answer:

D. Estimate $\sqrt{37}$