The trapezoid shown exists such that BC = 8 cm, AD = 12 cm, BC || EF || AD, and EF and the two diagonals intersect at a common point. Find EF

Question

geerky42 · Answer

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campbell_st · Answer

you need to look at the ratios in similar trapeziods.. 

if EF is parallel to AD and BC then you have 2 trapeziods

AEFD and EBCF

so looking at the ratios of sides 

$$\frac{EF}{AD}= \frac{BC}{EF} $$

given the known measurements

$$\frac{EF}{12} = \frac{8}{EF}$$

then after cross multiplying 

$$EF^2 = 96$$

which makes sense as the length of EF will be just less than 10, which is between the 2 known side lengths 8 and 12... 

I'll leave you to calculate the actual value of EF

geerky42 · Answer

@campbell_st Your answer is wrong, I have answer key and the answer is actually 9.6 (nearest tenth). From your answer, I got 9.8...