SOLUTION: Please help me solve this word problem. Geometry. The length of a rectangle is 2 cm more than 3 times its width. If the area of the rectangle is 95 cm2, find the dimensions of

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Question 98129: Please help me solve this word problem.
Geometry. The length of a rectangle is 2 cm more than 3 times its width. If the
area of the rectangle is 95 cm2, find the dimensions of the rectangle.
Thank you
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is 2 cm more than 3 times its width. If the
area of the rectangle is 95 cm2, find the dimensions of the rectangle.
:
Let x = width of the rectangle
:
It says,"The length of a rectangle is 2 cm more than 3 times its width." Therefore
Length = (3x + 2)
:
"area of the rectangle is 95 cm2,"
L * W = 95
Therefore:
(3x+2) * x = 95
:
3x^2 + 2x = 95
:
3x^2 + 2x - 95 = 0; a quadratic equation, solve using the quadratic formula
a = 3; b = 2; c = -95
:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
x+=+%28-2+%2B-+sqrt%28+2%5E2+-+4+%2A+3+%2A+-95+%29%29%2F%282%2A3%29+
:
x+=+%28-2+%2B-+sqrt%284+-+%28-1140%29+%29%29%2F%286%29+
:
x+=+%28-2+%2B-+sqrt%284+%2B+1140+%29%29%2F%286%29+; minus a minus is a plus
:
x+=+%28-2+%2B-+sqrt%281144+%29%29%2F%286%29+
Two solutions, but it's the positive solution we want here
x+=+%28-2+%2B+33.823%29%2F6
x+=+31.823%2F6
x = 5.305 is the width
:
Length = 3(5.305) + 2 = 17.915 is the length
:
:
Check solution:
5.305 * 17.915 = 95.0