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39 votes
39 votes
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?

User Mohammad Hassany
by
2.7k points

1 Answer

10 votes
10 votes

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:


(88-9x)/(7x-49)=(1)/(2)

and we solve for x so:


\begin{gathered} 176-18x=7x-49 \\ 176+49=18x+7x \\ 225=25x \\ (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}

User Hyunsoo
by
3.0k points
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