Question

1. determine the length of each hypotenuse.

a)
image of a right triangle with legs labeled ( a = 12 , \text{cm} ), ( b = 16 , \text{cm} ) and hypotenuse ( c )

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, the Pythagorean theorem states that \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse and \(a\), \(b\) are the legs of the right - triangle.
Here, \(a = 12\space\text{cm}\) and \(b=16\space\text{cm}\). So we substitute these values into the formula: \(c^{2}=12^{2}+16^{2}\).

Step2: Calculate the squares

First, calculate \(12^{2}=144\) and \(16^{2} = 256\). Then, \(c^{2}=144 + 256\).

Step3: Sum the values

\(144+256 = 400\), so \(c^{2}=400\).

Step4: Take the square root

To find \(c\), we take the square root of both sides. Since \(c\) represents the length of a side, we take the positive square root. So \(c=\sqrt{400}=20\space\text{cm}\).

Answer:

The length of the hypotenuse \(c\) is \(20\space\text{cm}\).