Question

1. consider the diagram.

find the values of x and y. if your answer cannot be expressed as a rational number, use
square root notation to enter the value.

Explanation:

Step1: Find the value of \(x\) using the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs of the right - triangle and \(c\) is the hypotenuse.
For the smaller right - triangle with legs \(8\) and \(5\), we have \(x=\sqrt{8^{2}+5^{2}}\).

$$x = \sqrt{64 + 25}=\sqrt{89}$$

Step2: Find the value of \(y\) using the Pythagorean theorem

For the larger right - triangle with legs \(8 + 4=12\) and \(5\), we have \(y=\sqrt{(8 + 4)^{2}+5^{2}}\).

$$y=\sqrt{12^{2}+5^{2}}=\sqrt{144+25}=\sqrt{169}=13$$

Answer:

\(x = \sqrt{89}\), \(y = 13\)