SOLUTION: a rectangular piece of cardboard measures 17cm by 14cm stripes of equal width are cutoff one side and one end. the area of the remaining piece is 108cm^2 find the width of the stri

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Question 1145923: a rectangular piece of cardboard measures 17cm by 14cm stripes of equal width are cutoff one side and one end. the area of the remaining piece is 108cm^2 find the width of the stripes removed?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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a rectangular piece of cardboard measures 17cm by 14cm
strips of equal width are cutoff one side and one end.
the area of the remaining piece is 108cm^2
find the width of the strips removed?
:
let x = the width of the strips
(17-x)(14-x) = 108
FOIL
238 - 17x - 14x + x^2 = 108
combine like terms
x^2 - 31x + 238 - 108 = 0
x^2 - 31x + 130 = 0
you can use the quadratic formula, a=1; b=-31; c=130, but this will factor to:
(x-5)(x-26) = 0
x = 5 cm is the reasonable solution here.
:
:
Check:
(17-5)*(14-5) =
12 * 9 = 108