SOLUTION: A rectangle with 90 square inches has length that is 2/3 of the width plus 4 inches. What are the lenght and width.

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Question 27994: A rectangle with 90 square inches has length that is 2/3 of the width plus 4 inches. What are the lenght and width. I know the answer through common sense they are width of 9 inches and length of 10 inches. How do I show how I got those answer with only the info above.
Thank you,
Dale
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Width = x
Length = 2x%2F3%2B4

Formula:
%282x%2F3%2B4%29%28x%29=90
2x%5E2%2F3%2B4x=90
Remove fraction by multiplfing the equation by 3
2x%5E2%2B12x-270=0
x%5E2%2B6x-135=0

a=1, b = 6 c=-135
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=%28-6%2B-sqrt%286%5E2-4%2A1%2A-135%29%29%2F%282%2A1%29
x=%28-6%2B-sqrt%2836%2B540%29%29%2F%282%29
x=%28-6%2B-sqrt%28576%29%29%2F%282%29
x=%28-6-24%29%2F2 or x=%28-6%2B24%29%2F2
remove the negative
x=9

2%289%29%2F3+%2B+4 = 10

Hence, the width is 9cm and the length is 10 cm.
Paul.