Question 200681
Please I need help with this. Find x if shaded area is 90.the (whole rectangle is shaded except for the holes) By developing and solving by factoring quadratic equation. The rectangle width is 2x-2, length is 3x, and there are 3 holes cut out with the width of x and length of x-1. I know l*w=A but how do you take out the hole squares?
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Area of rectangle = (3x)(2x-2)
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Area of one hole = x(x-1)
Three holes would then be 3x(x-1)
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"Shaded area" = "area of rectangle" - "area of holes"
90 = (3x)(2x-2) - 3x(x-1)
On the right side, distribute:
90 = (6x^2-6x) - (3x^2-3x)
90 = 6x^2-6x - 3x^2+3x
90 = 3x^2-3x
0 = 3x^2-3x-90
0 = x^2-x-30
Factoring:
0 = (x-6)(x+5)
x = {-5, 6}
Throwing out the negative solution we get:
x = 6