Question

What is the length of leg $y$ of the right triangle? A right triangle with hypotenuse $85$ and legs $84$ and $y$ are .

• A. $1$
• B. $9$
• C. $13$
• D. 26

Answer 1

The correct option is C

$13$

Explanation for the correct option.

Option (C):

Length of leg $y$ can be found using Pythagorean Theorem:

${\left(\text{hypotenuse}\right)}^2={\left({\text{leg}}_1\right)}^2+{\left({\text{leg}}_2\right)}^2$.

So,

$\begin{array}{rcl}{\left(85\right)}^2& =& {\left(84\right)}^2+{\left(y\right)}^2\\ & \Rightarrow & 7225=7056+y^2\\ & \Rightarrow & 169=y^2\\ & \Rightarrow & 13=y\end{array}$

The length of leg $y$ of the right triangle is $13\text{units}$.

Therefore, the correct option is Option (C).