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 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.
+128474 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
