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In the figure below, ABCD is a parallelogram, AD = 18 and DC = 27. Segments EG and FH are perpendicular to sides of the parallelogram as shown, and EG = 18. Determine FH.

 

 

 Dec 19, 2021
 #1
avatar+21 
+1

Let us consider the area of this parallelogram. The area of this paralleogram is EG * DC = 18*27 = 486. Another way to calculate the area of this paralleogram is BC * FH. We know that BC = AD = 18. Therefore, 18 * FH = 486, or FH = 27. 

 Dec 19, 2021
 #2
avatar+1696 
+2

Only in the case of a rectangle or a square, AD = EG

 Dec 19, 2021
 #3
avatar+75 
+2

As AD=EG, the diagram shown above must be a rectangle.
The area of a rectangle is defined as length*width.

AD*DC must be equal to EG*FH, since EG and FH are also perpendicular to sides AD and DC.

We know that AD=18, DC=27, and EG=18.

By setting FH=x, we get the equation

18*27=18x.

By dividing both sides by 18, we get x=27.

 Dec 19, 2021

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