Question

$\overline{\mathrm{GM}}$is a median of right $\Delta \mathrm{IRG}$

If $\mathrm{GM}=2\mathrm{y}+3$and $\mathrm{RI}=12-8\mathrm{y}$find the value of y.

Short answer

The value of y is $\frac{1}{2}$.

Step-by-step solution

Step 1. Description of step.

For the right-angled triangle, the median is half of the hypotenuse.

Therefore, $GM=\frac{RI}{2}$.

Step 2. Description of step.

Substitute $2y+3$for $GM$and $12-8y$for $RI$into $GM=\frac{RI}{2}$.

$\begin{array}{c}2y+3=\frac{12-8y}{2}\\ 2\left(2y+3\right)=12-8y\\ 4y+6=12-8y\\ 12y=6\end{array}$

Step 3. Description of step.

Divide each side of the obtained equation in steps 2 by 6 to find the value of y.

$\begin{array}{c}\frac{12y}{12}=\frac{6}{12}\\ y=\frac{1}{2}\end{array}$

Therefore, the value of y is $\frac{1}{2}$.