A rectangle is #6# units wide and #x-8# units long. It has the same area as a triangle with a height of #7# units and a base of #x-3# units. What is the area of the rectangle?

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Answer 1 · 2015-11-27T22:27:25

Rectangle Area #=lw#
Triangle Area #=1/2bh#

Set the two areas equal to each other, solve for x, then substitute x back into the area for the rectangle.

#6xx(x-8)=1/2xx7xx(x-3)#

Simplify ...

#6x-48=3.5x-10.5#

#2.5x=37.5#

#x=15#

Area of Rectangle #=6xx(x-8)=6xx(15-8)=42#

[Note: 42 is also the area of the triangle]

hope that helped