Question

two different squares have sides in the ratio a : b. what is the ratio of the areas of the squares? the ratio of the areas of the squares that corresponds to the side ratio a : b is

Explanation:

Step1: Recall the formula for the area of a square

The area of a square \(A = s^{2}\), where \(s\) is the side - length of the square.

Step2: Let the side - lengths of the two squares be \(a\) and \(b\)

For the first square with side - length \(s_1=a\), its area \(A_1=a^{2}\). For the second square with side - length \(s_2 = b\), its area \(A_2=b^{2}\).

Step3: Find the ratio of the areas

The ratio of the areas of the two squares is \(\frac{A_1}{A_2}=\frac{a^{2}}{b^{2}}\)

Answer:

\(a^{2}:b^{2}\)