Question

Mario is constructing a square dart board. It will consist of a smaller square centered in a larger square. The smaller square measures $4$ inches on each side. The ratio of the area of the smaller square to the area of the entire dart board is $\frac 49$. How long is the side of the larger square?

Answer 1

Answer:

6 inches.

Step-by-step explanation:

Let a represent side length of larger square.

We know that area of square is square of its side length, so area of the larger square will be $a^2$.

The area of smaller square would be $4^2$.

We will use proportions to solve our given problem.

$\frac{\text{Area of smaller square}}{\text{Area of larger square}}=\frac{4}{9}$

$\frac{4^2}{a^2}=\frac{4}{9}$

$\frac{16}{a^2}=\frac{4}{9}$

Cross multiply:

$4*a^2=16*9$

$\frac{4*a^2}{4}=\frac{16*9}{4}$

$a^2=36$

Take square root:

$a=\pm\sqrt{36}$

$a=\pm 6$

Since the length cannot be negative, therefore, the side length of larger square is 6 inches.