Question 80865: Hi, I'd greatly appreciate help with this word problem: The length of a rectangle is 4 cm more than 2 times its width. If the area of the rectangle is 90 cm^2, find the dimensions of the rectangle to the nearest thousandth.
Answer by praseenakos@yahoo.com(507)   (Show Source):
You can put this solution on YOUR website! QUESTION:
The length of a rectangle is 4 cm more than 2 times its width. If the area of the rectangle is 90 cm^2, find the dimensions of the rectangle to the nearest thousandth.
ANSWER:
Assume that width of the rectangle is 'x' cm.
Then two times width = 2x
4 cm more than 2 times its width = (2x + 4)cm
It is given that its length is 4 cm more than 2 times its width
So length of the rectangle = (2x + 4 ) cm.
Area of a rectangle is given by the formula, A = length * width
Here area is given that 90 cm^2
So we can write it as,
90 = (2x + 4 ) * x
==> 90 = 2x * x + 4 * x
==> 90 = 2x^2 + 4x
Subtract 90 from both sides of the equation, then we will obtain a quadratic equation.
==> 90 - 90 = 2x^2 + 4x - 90
==> 0 = 2x^2 + 4x - 90
2x^2 + 4x - 90 = 0
We can solve this equation using quadratic formula.
standard form of a quadratic equation is,
ax^2 + bx + c = 0 ---------------(2)
By quadratic formula, the solution is given by,
Comparing (1) and (2) we have,
a = 2, b = 4 and c = -90
so the solution is,
x = (-4 + 27.129)/4 or x = (-4 - 27.129 )/4
x = 23.129/4 or x = -41.129/4
( since negative values are not admisible here)
==> x = 5.782 cm
So width of the rectangle is 5.782 cm.
so width = 5.782 cm.
and length = 2x + 4 = 2 * (5.782) + 4 = 11. 564 + 4 = 15.564 cm
So the dimenstions of the given rectangle:
length = 15. 564 cm and
Width = 5.782 cm.
To check your answer, multiply lenth with breadth, then you will get 90 approximately.
Hope you understood.
Regards.
Praseena.
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