Question

Find EF in the trapezoid.

Answer 1

so hmmm alrite

the tickmarks on the left and right sides, simply mean, the sides are split evenly, that makes the segment EF the midsegment of the trapezoid

thus   $\bf \textit{midsegment of a trapezoid}\\\\ m=\cfrac{base1+base2}{2}\qquad \begin{cases} base1, base2=\textit{parallel sides}\\ ----------\\ base1=x+8\\ base2=58\\ m=6x \end{cases} \\\\\\ 6x=\cfrac{(x+8)+(58)}{2}\implies 6x=\cfrac{x+8+58}{2}\implies 12x=x+66 \\\\\\ 11x=66\implies x=\cfrac{66}{11}\implies x=6$

Answer 2

EF in the trapezoid = 36

The length of mid segment of trapezoid is given by the equation (1)

$\rm Length \; of \; mid \; segment \; of \; trapezoid = (b_1 +b_2)/2 ....(1)$

The given trapezoid ABCD  has following properties

AD and BC are the bases of the trapezoid.

Mid segment of trapezoid = EF

$\rm AD = x+8\\EF = 6x\\BC = 58$

$\rm b_1= AD \\b_2 = BC$

Using equation (1) we can write

$\rm EF = \dfrac{AD+ BC}{2}....(2)$

On putting values of EF , AD and BC in equation (2)  and solving for $\rm x$

$\rm 6x = \dfrac{x+8+58 }{2}$

$11x =66\\x =6$

So Length of EF = $\rm 6\times 6 = \bold {36}$

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