Question

The front of a box and the sticker label on it are similar rectangles. The front of the box has a width of 9 inches and a length of inches. Which dim bisons could be the dimensions of the sticker label ?

Answer 1

Answer:

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The formula for the perimeter for a rectangle is P = 2L + 2W

The formula for the area of a rectangle is A = LW

where L = length and W = width

 

P = 22 and A = 28

 

22 = 2L + 2W

28 = LW 

 

Rewriting the 2nd equation L = 28/W

Substituting this into the first equation

22=2(28/W) + 2W

 

Reworking the equation to eliminate the denominator

22W = 2(28) + 2W2

22W = 56 + 2W2

 

and

2W2 - 22W + 56 = 0

 

Dividing by 2

W2 - 11W + 28 = 0

(W-7)(W-4)

 

Set each factor equal to 0 and solve each for 0

W = 4, W = 7

 

If W = 4, then 2(L+4)=22

L = 7

 

The sticker is 7 cm by 4 cm