The areas of two squares are in the ratio 49 : 9. What is the ratio of their perimeters?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 7 : 3
The area of a square is \(a^2\) and its perimeter is \(4a\). So the ratio of sides is the square root of the ratio of areas, and the perimeters are in the same ratio as the sides.
\(a_1^2:a_2^2=49:9\)
\(a_1:a_2=\sqrt{49}:\sqrt{9}=7:3\)
Perimeters: \(4a_1:4a_2=7:3\)