**Problem:**

Find the length of the missing side of the trapezoid below.

*Give your answer in simplified form.*

donkey Apr 13, 2019

#1**+1 **

Draw a perpendicular line from the upper left corner to the base.

That makes a right triangle with one side = 3 and the hypotenuse = 7.

Use Pythagoras' Theorem to determine the third side.

x^{2} + 3^{2} = 7^{2}

x^{2} = 7^{2} – 3^{2}

x^{2} = 49 – 9

x = square root of 40 = 2 sqrt(10) A square root is plus and minus of course, but we disregard the negative answer.

.

Guest Apr 13, 2019

#2**+2 **

Drop a perpendicular height from the right of the side length of 5 to the base of 8. This would create a right-triangle with a hypotenuse of 7 units and a measure of one of the legs, 3 units. Using the Pythagorean theorem, we have \(7^2-3^2=49-9=\sqrt{40}=2\sqrt{10}.\)

.neworleans06 Apr 13, 2019

#3**+2 **

Draw a perpedicular to the base from the top left vertex

Call the intersection point of the base and this perpendicular, E

Call the top left vertex D and the bottom left vertex, F

So....we have right triangle DEF

EF [ 8 - 5] = 3 = a leg

And the hypotenuse FD = 7

So...DE is the missing leg = missing side

So...using the Pythagorean Theorem

DE = √ (7^2- 3^2] = √ [ 49 - 9 ] = √40 = √4 *√10 = 2√10 = missing side

CPhill Apr 13, 2019