SOLUTION: the perimeter of a rectangle is 108 cm. If the length is increased by 5 and the width is doubled. The perimeter becomes 182cm. Find it's dimension.

Algebra ->  Rectangles -> SOLUTION: the perimeter of a rectangle is 108 cm. If the length is increased by 5 and the width is doubled. The perimeter becomes 182cm. Find it's dimension.      Log On


   

Question 1007447: the perimeter of a rectangle is 108 cm. If the length is increased by 5 and the width is doubled. The perimeter becomes 182cm. Find it's dimension.
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
let l be length and w be width, then
2l + 2w = 108
2(l+5) + 2(2w) = 182
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simplify the second equation
2l + 10 + 4w = 182
2l + 4w = 172
now subtract the first equation from our simplified equation
2w = 64
w = 32
substitute for w in first equation and solve for l
2l + 2*32 = 108
2l + 64 = 108
2l = 44
l = 22
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length = 22 cm and width is 32 cm
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now check our answer by substituting for l and w in second equation
2(22+5) + 2(2*32) = 182
2*27 + 2*64 = 182
54 + 128 = 182
182 = 182
our answer checks