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Problem:

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

Give your answer in simplified form.

 Apr 13, 2019
 #1
avatar
+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.

 

x2 + 32  = 72

 

x2 = 72 – 32

 

x2 = 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.

 

.

 Apr 13, 2019
 #2
avatar+52 
+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 \(7^2-3^2=49-9=\sqrt{40}=2\sqrt{10}.\)

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 Apr 13, 2019
 #4
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I'm pretty sure that \(49-9\ne\sqrt{40}\) but you have the right idea.

Guest Apr 13, 2019
 #3
avatar+106519 
+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

 

 

 

cool cool cool

 Apr 13, 2019
 #5
avatar+64 
+1

Thanks, everyone!

 Apr 13, 2019

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