Question

Part D Some of the measurements of the triangular prism with a right triangle base are shown. 12 cm €! 24 cm 4 cm 42.com 12 cm What is the length of the hypotenuse of the base?

Answer 1

We take the base and the measures

H is the hypotenuse, we can notices the line makes a right triangle then we can use pythagoras

$a^2+b^2=h^2$

where a and b are sides of the triangle and h the hypotenuse, then replacing

$(12)^2+(4)^2=H^2$

simplify

$\begin{gathered} 144+16=H^2 \\ 160=H^2 \end{gathered}$

and use roots to solve H

$\begin{gathered} \sqrt[]{160}=\sqrt[]{H^2} \\ \\ 4\sqrt[]{10}=H \\ \\ H=4\sqrt[]{10}\approx12.65 \end{gathered}$

the hypotenuse of the base is 12.65 centimeters