Trapezoid geometry problem

Hi! I recently came across this question which I have been having a hard time with. I have no idea on how to even approach this problem so I have not made much progress towards the solution. Here is the question: The diagonals of a trapezoid have lengths 17 and 15, and the segment connecting the midpoints of the bases has a length of 4. The height of the trapezoid can be expressed as x√y/y. Find x + y.

#Geometry

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
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Comments

Hint: Solve triangle with AB=15, AC = 17 and median AM =4. Its height is the same as height of your trapezoid. Second hint: area of this triangle is the same as area of the Pythagorean triple: (8,15,17).

Maria Kozlowska - 1 year, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$