Square ABCD has side lengths of 13 units. Point E lies in the interior of the square such that AE=5 units and BE=12 units. What is the distance from E to side AD? Express your answer as a mixed number.
The answer is 25/13. I need an explanation why. If you can't do it, please do NOT post some random answer just to get points.

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MichaelLiuid MichaelLiuid

Mathematics

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Square ABCD has side lengths of 13 units. Point E lies in the interior of the square such that AE=5 units and BE=12 units. What is the distance from E to side AD? Express your answer as a mixed number.
The answer is 25/13. I need an explanation why. If you can't do it, please do NOT post some random answer just to get points.

Sagot :

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Dieneid Dieneid · Answer 1

If you draw a diagram, you'll see that triangle AEB is a right triangle with lengths 5, 12, and 13. Let's call F the point where E meets side AD, so the problem is to find the length of EF. By Angle-Angle Similarity, triangle AFE is similar to triangle BEA. (the right angles are congruent, and both angle FAE and ABE are complementary to angle BAE) Since they're similar, the ratios of their side lengths is the same. EF/EA=EA/AB (they're corresponding side lengths of similar triangles). Substitute them with known lengths: EF/5 = 5/13
EF=5*(5/13)=25/13=1 12/13
I'm sorry I couldn't provide a diagram.
If you have any questions just ask. :)