SOLUTION: The heights and bases of two geometric shapes are modeled by the expressions shown. Triangle: h=3x+2 and b=2x+3 Parallelogram: h=3x+4 and b=3x+2 What expression represe

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The heights and bases of two geometric shapes are modeled by the expressions shown. Triangle: h=3x+2 and b=2x+3 Parallelogram: h=3x+4 and b=3x+2 What expression represe      Log On

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Question 947213: The heights and bases of two geometric shapes are modeled by the expressions shown.
Triangle: h=3x+2 and b=2x+3
Parallelogram: h=3x+4 and b=3x+2
What expression represents the number of units by which the area of the parallelogram is greater than the area of the triangle?

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

by definition:
A parallelogram is a 4-sided figure formed by two pairs of parallel lines.Opposite sides are equal in length and opposite angles have equal measure.
The area of a parallelogram is A+=+b+%2A+h, the area of a triangle must be one-half the area of a parallelogram.
Thus, the formula for the area of a triangle is: A+=+%281%2F2%29b+%2A+h
if given
Triangle: h=3x%2B2 and b=2x%2B3
then
A%5Bt%5D+=+b+%2A+h
A%5Bt%5D+=+%281%2F2%29%282x%2B3%29%2A%283x%2B2%29
A%5Bt%5D+=+%281%2F2%29%2A%286x%5E2%2B4x%2B9x%2B6%29
A%5Bt%5D+=+%281%2F2%29%2A%286x%5E2%2B13x%2B6%29
A%5Bt%5D+=+3x%5E2%2B6.5x%2B3
and
Parallelogram: h=3x%2B4 and b=3x%2B2
A%5Bp%5D+=+%283x%2B2%29%2A%283x%2B4%29
A+%5Bp%5D=+9x%5E2%2B12x%2B6x%2B8
A%5Bp%5D+=+9x%5E2%2B18x%2B8

What expression represents the number of units by which the area of the parallelogram is greater than the area of the triangle?
A%5Bt%5D+=+3x%5E2%2B6.5x%2B3
A%5Bp%5D+=+9x%5E2%2B18x%2B8
find the difference:
A%5Bp%5D-A%5Bt%5D+=9x%5E2%2B18x%2B8-%283x%5E2%2B6.5x%2B3%29
A%5Bp%5D-A%5Bt%5D+=9x%5E2%2B18x%2B8-3x%5E2-6.5x-3
A%5Bp%5D-A%5Bt%5D+=6x%5E2%2B11.5x%2B5
6x%5E2%2B11.5x%2B5=> expression represents the number of units by which the area of the parallelogram is greater than the area of the triangle