SOLUTION: 24 the length of a rectangle is 3 cm longer that twice the width. The area of the rectangle is 90 sq cm. Find the length and width of the rectangle.

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Question 69264: 24 the length of a rectangle is 3 cm longer that twice the width. The area of the rectangle is 90 sq cm. Find the length and width of the rectangle.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=width of rectangle
Then 2x=twice the width of the rectangle
And the length =2x+3; three cm longer that twice the width
Area of rectangle =l*w
Area of rectangle=(2x+3)(x)
%282x%2B3%29%28x%29=90 get rid of parens
2x%5E2%2B3x=90 subtract 90 from both sides
2x%5E2%2B3x-90=0 quadratic in standard form
solve by using the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A2%2A%28-90%29+%29%29%2F%282%2A2%29+
x+=+%28-3+%2B-+sqrt%28729%29%29%2F%284%29+
x+=+%28-3+%2B-+27%29%2F%284%29+
x+=+%28-3+%2B27%29%2F%284%29+
x=24%2F4
x=6%29 cm -----------------width of rectangle
2x%2B3=2%2A6%2B3=15 cm------------------length of rectangle
We will discount the negative value for x
CK
Area of rectangle =l*w=6*15=90 sq cm ----ok
Hope this helps----ptaylor