Question

graded quiz: polygons and triangles
what is the length of the hypotenuse of the right triangle abc in the figure?
a) 6.2
b) 7.2
c) 5.8

Explanation:

Step1: Use the geometric mean theorem (altitude-on-hypotenuse theorem)

In a right - triangle \(ABC\) with right angle at \(C\) and altitude \(CD\), we know that \(AC^{2}=AD\times AB\). Let \(AB = x\), then \(6^{2}=5\times x\).

Step2: Solve for \(AB\)

From \(36 = 5x\), we get \(x=\frac{36}{5}=7.2\)

Answer:

B. 7.2