Mathematics
FionaEaster
55

The length of a rectangle is 7 inches more than its width. The area of the rectangle is equal to 2 inches less than 5 times the perimeter . What is the length and width

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(1) Answers
GalaxyVanz

Let the width be w, then the length is w+7 units. The area of the rectangle is [latex]A=w(w+7)= w^{2}+7w [/latex]. The perimeter of the rectangle is:  P = 2(Width + Length)=2(w+w+7)=2(2w+7)=4w+14 "The area of the rectangle is equal to 2 inches less than 5 times the perimeter." means that: A = 5P - 2 [latex]w^{2}+7w=5(4w+14)-2[/latex] [latex]w^{2}+7w=20w+70-2[/latex] [latex]w^{2}-13w-68=0[/latex] to solve the quadratic equation, let's use the quadratic formula let a=1, b=-13, c=-68 [latex]D= b^{2} -4ac=169-4(1)(-68)=169+272=441[/latex] the root of the discriminant is 21 the roots are w1=(13+21)/2=34/2=17 and w2=(13-21)/2=-8/2=-4, which cannot be the width. The width is 17 units, and the length is 17+7=24 units Answer: w=17, l=24

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