Question

pythagorean theorem converse hw1.2b
#10. which of the following could be the perimeters of the three squares below?
a 12 ft², 16 ft², and 20 ft²
b 20 ft², 16 ft² and 24 ft²
c both a and b
d neither a nor b

Explanation:

Step1: Recall Pythagorean theorem

For three squares with side - lengths \(a\), \(b\), and \(c\) (where the squares are arranged as in the right - triangle related figure), if the sides of the right - triangle are \(a\), \(b\), and \(c\) (with \(c\) as the hypotenuse), then \(a^{2}+b^{2}=c^{2}\). The area of a square with side - length \(s\) is \(A = s^{2}\). So, if the areas of the three squares are \(A_1\), \(A_2\), and \(A_3\), then \(A_1 + A_2=A_3\) for the squares related to a right - triangle.

Step2: Check option A

For option A, \(A_1 = 12\), \(A_2=16\), and \(A_3 = 20\). Calculate \(A_1+A_2\): \(12 + 16=28
eq20\).

Step3: Check option B

For option B, \(A_1 = 20\), \(A_2 = 16\), and \(A_3=24\). Calculate \(A_1 + A_2\): \(20+16 = 36
eq24\).

Answer:

D. Neither A nor B