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