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# help

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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.

Nov 6, 2019

#1
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The pythagorean theorem (a^2 + b^2 = c^2) can be used to calculate the length of the side DE. Once the right triangle is completed, the distance from the hypotenuse to the opposite corner can be calculated. The answer is 25/13.

Nov 6, 2019
#2
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AB  = 13

AE  = 5

BE  = 12

So    triangle  ABE  is a 5 - 12 - 13 right triangle

The area  of  this triangle  =  (1/2)(12)(5)  = 30

The base of the triangle  = AB  = 13

So

30  = (1/2)base * altitude

60 = 13 * altitude

60/13  = altitude

Call the altitude EF

And using the Pythagorean Theorem

BF  =

sqrt ( BE^2  -  EF^2)  =

sqrt (12^2 - (60/13)^2)  =

sqrt  (144 - 3600/169)  =

sqrt (144 * 169 - 3600) / 13  =

sqrt (20736) / 13  =

144/13

So....the distance that  E  is from AD   =

AB - BF  =

13  - 144/13   =

[169 - 144] / 13   =

25/13 units  =

1 + 12/13  units   Nov 6, 2019