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Papessa [141]
3 years ago
12

Use the three steps to solve the problem. the length of a rectangle is 2 inches less than 3 times the number of inches in its wi

dth. if the perimeter of the rectangle is 28 inches, what is the width and length of the rectangle?
Mathematics
1 answer:
Tems11 [23]3 years ago
3 0
Let the width of the rectangle be w.

Let the length be l.

l = 3w - 2

Given,

Perimeter = 28 

2*( l + w ) = 28

2*( 3w -2 + w ) = 28 

4w - 2 = 14  [ Dividing both sides by 2 ]

2w - 1 = 7 [ Dividing both sides by 2 ]

2w = 8

w = 4.

Thus,

l = 3w -2 = 3*4 - 2 = 12 - 2 = 10

Therefore, the length is 10 inches and the width is 4 inches.
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We can factor by grouping. To do so, we multiply the leading coefficient with the constant at the end. In other words, a times c (ax^2 + bx + c).

15*-4 = -60

Now we need to split the b term into two pieces that multiply to -60 and add to 4.

-6 and 10 will work.

Now group one part of b with the 15x^2 and the other part with -4.

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Now factor both terms.

5x(3x+2) - 2(3x+2)

3x+2 is one of our factors and 5x-2 is the other.

(3x+2)(5x-2)=0

Now just find the zeros.

3x+2 = 0
3x = -2
x = -2/3

And

5x-2 = 0
5x = 2
x = 2/5

So the answer is x = -2/3 and x = 2/5






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