SOLUTION: 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

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.

RELATED QUESTIONS
Please help me solve this word problem. Geometry. The length of a rectangle is 2 cm... (answered by ankor@dixie-net.com)

Please help me solve this problem. I have no idea how to arrange word problems . The... (answered by stanbon,MathLover1)

The length of a rectangle is 4 cm more than 2 times its width. If the area of the... (answered by ptaylor)

The length of a rectangle is 7.6 cm more than 3 times the width. If the perimeter of the... (answered by unlockmath)

how can i solve this problem???? the length of a rectangle is 2 cm more than four... (answered by rapaljer)

I am having major problems with this word problem and need some help The length of a... (answered by scott8148)

Hi! I really need help with this problem that I am currently stuck on. Could you help me? (answered by MathLover1,KMST)

Hi could someone please help with this word problem. The length of a rectangle is 8... (answered by ewatrrr)

I am really having troubles with these word problems. The length of a rectangle is 6... (answered by josmiceli)