Question

if a = 5 and b = 7, what is the area of square c?
options: 8.6, 74, 6241, 12

Explanation:

Step1: Identify the theorem

This is a right - triangle - square relationship problem. By the Pythagorean theorem, for a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). And the area of square \(c\) is \(c^{2}\) (since the area of a square is side length squared, and the side length of square \(c\) is the hypotenuse \(c\) of the right triangle).

Step2: Substitute the values

Given \(a = 5\) and \(b=7\), we calculate \(a^{2}+b^{2}\). First, calculate \(a^{2}=5^{2}=25\) and \(b^{2}=7^{2} = 49\). Then, \(a^{2}+b^{2}=25 + 49=74\). So the area of square \(c\) is \(74\).

Answer:

74