Question

6. Solve for x and y. I H EH = FH = HG

Answer 1

In the figure shown, triangle EHF is an isosceles triangle. Lines EH equals FH (as shown by the strokes on the line segments). Therefore;

$\begin{gathered} EH=FH \\ 9x-2=7x+4 \\ \text{Collect like terms and you'll have;} \\ 9x-7x=4+2 \\ 2x=6 \\ \text{Divide both sides by 2} \\ x=3 \\ \text{Also, triangle EGH is isosceles, therefore;} \\ EH=HG \\ 9x-2=5y \\ 9(3)-2=5y \\ 27-2=5y \\ 25=5y \\ \text{Divide both sides by 5} \\ 5=y \end{gathered}$

Therefore x = 3

y = 5