Question

1. use the picture to answer the questions below.

a) if a = 3 and b = 4, what is the area of square a and square b?
b) what is the area of square c?
c) what is the side length of square c?

Explanation:

Step1: Calculate area of Square A

The side - length of Square A is \(a = 3\). The area of a square is \(A=a^{2}\), so \(A_{A}=3^{2}=9\).

Step2: Calculate area of Square B

The side - length of Square B is \(b = 4\). The area of a square is \(A = b^{2}\), so \(A_{B}=4^{2}=16\).

Step3: Calculate area of Square C

By the Pythagorean theorem, if the sides of the right - triangle are \(a\) and \(b\), and the hypotenuse is \(c\), then \(c^{2}=a^{2}+b^{2}\). The area of Square C is \(A_{C}=a^{2}+b^{2}\). Substituting \(a = 3\) and \(b = 4\), we get \(A_{C}=3^{2}+4^{2}=9 + 16=25\).

Step4: Calculate side - length of Square C

Since the area of Square C is \(A_{C}=c^{2}=25\), then \(c=\sqrt{25}=5\).

Answer:

a) Area of Square A is 9, Area of Square B is 16.
b) Area of Square C is 25.
c) Side - length of Square C is 5.