SOLUTION: 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

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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