Question

think about the process the length of a rectangle is twice the width. the area of the rectangle is 88 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 $sqrt{44}$.
b. estimate $sqrt{88}$.
c. estimate $\frac{sqrt{88}}{4}$.
d. estimate $\frac{sqrt{44}}{4}$.
the rectangle is $square$ units long and $square$ units wide

Explanation:

Step1: Define variables for rectangle

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

Step2: Set up area equation

Area: $w \times 2w = 88$
$2w^2 = 88$

Step3: Solve for $w^2$

$w^2 = \frac{88}{2} = 44$

Step4: Relate to square side length

Each square has area equal to $w^2=44$, so side length = $\sqrt{44}$

(rectangle dimensions):

Step1: Estimate width $w$

$w = \sqrt{44}$, $6^2=36$, $7^2=49$, so $6 < \sqrt{44} < 7$
$\sqrt{44} \approx 6.6$

Step2: Calculate length $2w$

$2w = 2 \times 6.6 = 13.2$

Answer:

A. Estimate $\sqrt{44}$

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