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?
Accepted Solution
A:
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 [tex]a^2[/tex].The area of smaller square would be [tex]4^2[/tex].We will use proportions to solve our given problem.[tex]\frac{\text{Area of smaller square}}{\text{Area of larger square}}=\frac{4}{9}[/tex][tex]\frac{4^2}{a^2}=\frac{4}{9}[/tex][tex]\frac{16}{a^2}=\frac{4}{9}[/tex]Cross multiply:[tex]4*a^2=16*9[/tex][tex]\frac{4*a^2}{4}=\frac{16*9}{4}[/tex][tex]a^2=36[/tex]Take square root:[tex]a=\pm\sqrt{36}[/tex][tex]a=\pm 6[/tex]Since the length cannot be negative, therefore, the side length of larger square is 6 inches.