Question

The area of a right triangle is 10,710 square inches. The height of the right triangle is 612 inches.The length of the hypotenuse of the right triangle is ___ inches.

Answer 1

We have to use the formula for the area of a triangle

`A=(b\cdot h)/(2)`

Where A = 10,710 and h = 612, let's find b

`\begin{gathered} 10,710=(b\cdot612)/(2) \\ 10,710=306b \\ b=(10,710)/(306) \\ b=35 \end{gathered}`

Now, we use the base and height, which are legs, to find the hypotenuse using Pythagorean's Theorem

`\begin{gathered} h^2=612^2+35^2 \\ h=\sqrt[]{374,544+1,225} \\ h=\sqrt[]{375,769} \\ h=613 \end{gathered}`

Hence, the hypotenuse of the right triangle is 613 inches.