Question

if a right triangle has one side that measures 12 cm and one side that measures 5 cm, what is the measure of the hypotenuse?
a 13 cm
b 17 cm
c \\( \sqrt { 119 } \\) cm
d \\( \sqrt { 139 } \\) cm

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the Pythagorean theorem is \(a^2 + b^2 = c^2\), where \(a\) and \(b\) are the legs, and \(c\) is the hypotenuse. Here, \(a = 5\) cm and \(b = 12\) cm.

Step2: Substitute values into the formula

Substitute \(a = 5\) and \(b = 12\) into \(a^2 + b^2 = c^2\). So we have \(5^2 + 12^2 = c^2\). Calculate \(5^2 = 25\) and \(12^2 = 144\). Then \(25 + 144 = c^2\), which simplifies to \(169 = c^2\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{169}=13\) cm.

Answer:

A. 13 cm