Question

The hypotenuse of a $45°-45°-90°$ triangle measures $10\sqrt{5}\mathrm{in}.$.

What is the length of one leg of the triangle?

Answer 1

Find the length of one leg:

Given, a right triangle with hypotenuse $10\sqrt{5}\mathrm{in}.$

Let the side of triangle be, $x$.

Applying Pythagorean theorem ${\left(\mathrm{hypotenuse}\right)}^2={\left(\mathrm{perpendicular}\right)}^2+{\left(\mathrm{base}\right)}^2$:

$$\begin{gathered} x^2+x^2={\left(10\sqrt{5}\right)}^2 \\ 2x^2=500 \\ {x}^2=250 \\ x=\pm 5\sqrt{10} \end{gathered}$$

Since, length of a side can not be negative,

Hence, the side of triangle is $\mathbf{5}\sqrt{\mathbf{10}}\mathbf{}\mathbf{in}\mathbf{.}$