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a rectangular shelf has a perimeter of 46 inches. its area is 76 square inches. what are the dimensions of the shelf?

Step-by-step explanation:

l - length

w - width

The formula of a perimeter of a rectangle: P = 2(l + w)

The formula of an area of a rectangle: A = lw

We have P = 46in and A = 76in² Substitute:

(1)     2(l + w) = 46

(2)    lw = 76

2(l + w) = 46     divide both sides by 2

l + w = 23          subtract w from both sides

l = 23 - w

subtitute it to (2):

(23 - w)w = 76              use the distributive property

23w - w² = 76              subtract 76 from both sides

-w² + 23w - 76 = 0           change the signs

w² - 23w + 76 = 0

w² - 4w - 19w + 76 = 0

w(w - 4) - 19(w - 4) = 0

(w - 4)(w - 19) = 0 ⇔ w - 4 = 0 or w - 19 = 0

w - 4 = 0           add 4 to both sides

w = 4

w - 19 = 0           add 19 to both sides

w = 19

Put the values of w to (1):

l = 23 - 4 = 19 or l = 23 - 19 = 4

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is there a picture

step-by-step explanation: