How do I find the area of ABCD and solve for x?

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embizze | High School Teacher | (Level 2) Educator Emeritus

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Assume that ABCD is a parallelogram (hopefully this is given in the problem); Label the point where the perpendicular dropped from C to the extension of AD as F and the angle of the right triangle containing side x as E:

(1) The area of a parallelogram is A=bh where b is the base (one of the sides) and h is the height (the perpendicular distance from the base to the side opposite.)

Choose BC=7.5 as the base. Then CF=4 is the height.

The area of the parallelogram is (7.5)(4)=30 square units.

(2) Traingles CDF and ADE are similar by AA ~ (vertical angles and the right angles.) So `(CD)/(AD)=(DF)/(DE)=(CF)/(AE)`

CD=5,AD=7.5,CF=4, and AE=x

`5/7.5=4/x==>5x=4(7.5) ==> x=(4(7.5))/5=6`

So x=6.