Algebra II Area Problem?

Question

Find the dimensions of a rectangle if the area is 50m^2, the width is x-3, and the length is x+2.

Answer 1

area is 50m²,

the width is x-3,

and the length is x+2.

Then area of the rectangle =  ( x-3 )(x+2) = 50

There fore

x²+2x-3x-6 = 50

Simplfy

x²-x-6 = 50

Subtract 50 from each side.

x²- x - 6 -50 = 50 - 50

x²- x - 56 = 0

x²- 8x +7x - 56 = 0

Take out common factors.

x( x-8 ) +7( x-8) = 0

Take out common factors.

( x+7)( x-8 ) = 0

There fore

x+7 = 0  or  x-8 = 0

x =-7 or x = 8

There fore  x = -7 or  8