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gladu [14]
2 years ago
12

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
Mathematics
1 answer:
fredd [130]2 years ago
6 0
Let the width be w, then the length is w+7 units.

The area of the rectangle is A=w(w+7)= w^{2}+7w.

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

w^{2}+7w=5(4w+14)-2

w^{2}+7w=20w+70-2

w^{2}-13w-68=0

to solve the quadratic equation, let's use the quadratic formula

let a=1, b=-13, c=-68

D= b^{2} -4ac=169-4(1)(-68)=169+272=441

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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I understand the the question you are looking for is :

Cross-multiplication is helpful in:

a. quadratic equations

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c. linear equations

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please select the best answer from the choices provided a b c d

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