Question

triangle xyz is shown below. what is the length, to the nearest tenth of a centimeter, xy? 3 of 11 questio 15.5 cm 7.0 cm 13.3 cm 10.1 cm

Explanation:

Step1: Find the length of the base segment adjacent to \( YZ \)

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) for the right - triangle with hypotenuse \(YZ = 7\) and height \(4\). Let the base segment be \(a\). Then \(a=\sqrt{7^{2}-4^{2}}=\sqrt{49 - 16}=\sqrt{33}\approx5.7\)

Step2: Find the length of the base segment adjacent to \(XY\)

The total base \(XZ=15\), so the base segment adjacent to \(XY\) is \(b = 15-5.7 = 9.3\)

Step3: Calculate the length of \(XY\)

Use the Pythagorean theorem for the right - triangle with base \(b = 9.3\) and height \(4\). Then \(XY=\sqrt{9.3^{2}+4^{2}}=\sqrt{86.49+16}=\sqrt{102.49}\approx10.1\)

Answer:

\(10.1\space cm\) (the fourth option)