Question

the diagram shows a right triangle and three squares. the area of the largest square is 36 units². which could be the areas of the smaller squares? choose all answers that apply. 6 and 30 8 and 28 4 and 16

Explanation:

Step1: Recall the Pythagorean theorem

In a right - triangle, if the side lengths of the squares are \(a\), \(b\), and \(c\) (where \(c\) is the side length of the square on the hypotenuse), then \(a^{2}+b^{2}=c^{2}\). The area of a square is \(A = s^{2}\) (where \(s\) is the side length of the square). So, if the areas of the squares are \(A_1\), \(A_2\), and \(A_3\) (with \(A_3\) being the area of the largest square), then \(A_1 + A_2=A_3\).

Step2: Check each option

• Option A:

If \(A_1 = 6\) and \(A_2=30\), then \(A_1 + A_2=6 + 30=36\).

• Option B:

If \(A_1 = 8\) and \(A_2 = 28\), then \(A_1+A_2=8 + 28=36\).

• Option C:

If \(A_1 = 4\) and \(A_2=16\), then \(A_1 + A_2=4+16 = 20
eq36\).

Answer:

A. 6 and 30, B. 8 and 28