Question

In the diagram below of triangle FGH, J is a midpoint of FG and K is a midpointof GH. If JK = 88 - 9x, and FH = 7x – 49, what is the measure of JK?

Answer 1

In this problem we know that tha triangle FGH is similar to JGK because the have the same angles so we know that the rratio between their sides will be a constant so:

so we have that:

$\frac{88-9x}{7x-49}=\frac{1}{2}$

and we solve for x so:

$\begin{gathered} 176-18x=7x-49 \\ 176+49=18x+7x \\ 225=25x \\ \frac{225}{25}=x \\ 9=x \end{gathered}$

So finally with the value of X we can calculate JK so:

$\begin{gathered} JK=88-9(9) \\ JK=88-81 \\ JK=7 \end{gathered}$