Question

what is the missing side length?
first find the area of the two smaller squares and use them to find the area of the larger square. input the areas. then click done.
a =
a =
12
x
9
a = ?

Explanation:

Step1: Calculate the area of the square with side length 9

The area of a square is \(A = s^{2}\), where \(s\) is the side - length. For \(s = 9\), \(A=9^{2}=81\).

Step2: Calculate the area of the square with side length 12

Using the formula \(A = s^{2}\), for \(s = 12\), \(A = 12^{2}=144\).

Step3: Calculate the area of the larger square

By the Pythagorean theorem (the sum of the areas of the two smaller squares is equal to the area of the larger square in a right - triangle - related square - area problem), if the areas of the two smaller squares are \(A_1\) and \(A_2\), and the area of the larger square is \(A\), then \(A=A_1 + A_2\). Substituting \(A_1 = 81\) and \(A_2=144\), we get \(A=81 + 144=225\).

Answer:

The area of the square with side length 9 is \(81\), the area of the square with side length 12 is \(144\), and the area of the larger square is \(225\).