Question

Find the value of each variable for the right triangles. make sure all answers are in reduced radical form. show your work.

Answer 1

Hi there! The answer is 3 multiplied by the square root of 13.

Using the following theorem (Pythagorean Theorem), with a and b representing rectangular sides and c representing the hypotenuse, and the numbers from the picture, we get the following:

${a}^{2} + {b}^{2} = c {}^{2}$

Fill in the numbers
${6}^{2} + { 9}^{2} = c {}^{2}$

Work out the powers
$36 + 81 = {c}^{2}$

Add up
${c}^{2} = 117$

Take the square root of both sides.
$c = \sqrt{117} = 3 \sqrt{13}$