Question

I cannot find out EF for the life of me! Can someone help

Answer 1

Since the segments AE and EB are congruent and DF and FC are congruent, the trapezoid ABCD and EBCF are similar.

Therefore the proportion between the top bases of the trapezoids is the same as the bottom bases of the trapezoids.

So we have:

`\begin{gathered} (AD)/(EF)=(EF)/(BC) \\ \\ (5)/(3x+7)=(3x+7)/(7x+6) \\ 5\cdot(7x+6)=(3x+7)^2 \\ 35x+30=9x^2+42x+49 \\ 9x^2+7x+19=0 \end{gathered}`

Finding the roots using the quadratic formula, we have:

`\begin{gathered} a=9,b=7,c=19 \\ \\ x_1=\frac{-b+\sqrt[]{b^2-4ac}}{2a}=\frac{-7+\sqrt[]{49-4\cdot9\cdot19}}{18} \end{gathered}`