SOLUTION: A rectangle with a width of (-2x + 1) feet and a length of (-3x +4) feet, has an area of 450 square feet. What is the rectangle's width and length?

Algebra ->  Rectangles -> SOLUTION: A rectangle with a width of (-2x + 1) feet and a length of (-3x +4) feet, has an area of 450 square feet. What is the rectangle's width and length?      Log On


   



Question 1010081: A rectangle with a width of (-2x + 1) feet
and a length of (-3x +4) feet, has an area of
450 square feet. What is the rectangle's
width and length?

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

W=%28-2x+%2B+1%29 feet
L=+%28-3x+%2B4%29 feet,
A=450 square feet
A=L%2AW
450=%28-3x+%2B4%29%2A%28-2x+%2B+1%29
450=%28-3x%29%28-2x%29+%2B+%28-3x%291%2B4%28-2x%29%2B4%2A1%29
450=6x%5E2+-3x-8x%2B4
450=6x%5E2-11x%2B4
0=6x%5E2-11x%2B4-450
0=6x%5E2-11x-446...use quadratic formula

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-11%29+%2B-+sqrt%28+%28-11%29%5E2-4%2A6%2A%28-446%29+%29%29%2F%282%2A6%29+
x+=+%2811+%2B-+sqrt%28+121%2B10704+%29%29%2F12+
x+=+%2811+%2B-+sqrt%28+10825+%29%29%2F12+
x+=+%2811+%2B-+104.04%29%2F12+
we will need only negative solution since in given length and width coefficient of x is negative number:
x+=+%2811+-+104.04%29%2F12+
x+=++-93.04%2F12+
x+=++-7.753333333333333..round it
highlight%28x+=++-7.75%29+
now find the length and the width
W=-2%2A%28-7.75%29+%2B+1 feet=>W=15.5+%2B+1feet =>highlight%28W=16.5+%29
L=+-3%28-7.75%29+%2B4 feet =>L=+23.25+%2B4 feet=>highlight%28L=+27.25+%29 feet

check the area:
27.25%2A16.5=449.625 rounded to 450