Question 80995: the length of a rectangle is 5 cm more than 3 times its width. If the area of the rectangle is 95 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! The length of a rectangle is 5 cm more than 3 times its width. If the area of the rectangle is 95 cm^2, find the dimensions of the rectangle to the nearest thousandth.
ANSWER:
Assume that width of the rectangle is 'x' cm.
Then 3 times width = 3x
5 cm more than 3 times its width = (3x + 5)cm
It is given that its length is 5cm more than 3 times its width
So length of the rectangle = (3x + 5) cm.
Area of a rectangle is given by the formula, A = length * width
Here area is given that 95 cm^2
So we can write it as,
90 = (3x + 5 ) * x
==> 95 = 3x * x + 5 * x
==> 95 = 3x^2 + 5x
Subtract 95 from both sides of the equation, then we will obtain a quadratic equation.
==> 95 - 95 = 3x^2 + 5x - 95
==> 0 = 3x^2 + 5x - 95
3x^2 + 5x - 95 = 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 = 3, b = 5 and c = -95
so the solution is,
x = (-4 + 34.14)/6 or x = (-4 - 34.13 )/6
x = 30.14/6 or x = -38.13/6
( since negative values are not admisible here)
==> x = 5.023 cm
So width of the rectangle is 5.023 cm.
so width = 5.023 cm.
and length = 3x + 5 = 3 * (5.782) + 5 = 15.069 + 5 = 20.069 cm
So the dimenstions of the given rectangle:
length = 20.069 cm and
Width = 5.023 cm.
To check your answer, multiply length with breadth, then you will get 95 approximately.
Hope you understood.
Regards.
Praseena.
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