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The perimeter of a rectangle is 172 meters. Find the length and width if the length is an even integer and the width is 3 times the next consecutive even integer.

User IanJ
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1 Answer

2 votes

Answer:

length = 20 meters

width = 66 meters

Explanation:

P = perimeter. l = length. w=width

P = 2l + 2w ==> perimeter formula

Consecutive integers have a difference of 2 ( 4 - 2 = 2 )

Hence, the width(w) in terms of length(l) is:

w = 3 * (l + 2)

w = 3l + 3*2 ==> distribute 3 to l and 2

w = 3l + 6 ==> simplify

P = 2l + 2(3l + 6) ==> substitute w=3l + 6 into the equation P = 2l + 2w

P = 2l + 2*3l + 2*6 ==> distribute 2 to 3l and 6

P = 2l + 6l + 12

P = 8l + 12

172 = 8l + 12 ==> substitute 172 for P since the perimeter is 172 meters

160 = 8l ==> subtract 12 on both sides

l = 20 ==> divide both sides by 8

length = 20 meters

Now solve for the width:

w = 3(20) + 6 ==> substitute l=20 in w = 3l + 6

w = 60 + 6 ==> simplify

w = 66

width = 66 meters

User Tangoo
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