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?

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 .

The area of smaller square would be .

We will use proportions to solve our given problem.

Cross multiply:

Take square root:

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