Question

Brody calculated the area of a square to be 16/36 square foot.

Which shows the side length of the square?

A) 2/9 ft
B) 1/3 ft
C) 4/9 ft
D) 2/3 ft

Answer 1

To find the side length of a square when the area is given, we use the formula for the area of a square:

\[
\text{Area} = \text{side length}^2
\]

Given that the area is \( \frac{16}{36} \) square foot, we can set up the equation:

\[
\text{side length}^2 = \frac{16}{36}
\]

Next, we simplify \( \frac{16}{36} \):

\[
\frac{16}{36} = \frac{4}{9} \quad (\text{by dividing both numerator and denominator by 4})
\]

Now we have:

\[
\text{side length}^2 = \frac{4}{9}
\]

To find the side length, we take the square root of both sides:

\[
\text{side length} = \sqrt{\frac{4}{9}} = \frac{\sqrt{4}}{\sqrt{9}} = \frac{2}{3}
\]

Thus, the side length of the square is:

\[
\frac{2}{3} \text{ ft}
\]

The correct answer is:

**D) \( \frac{2}{3} \) ft**