SOLUTION: HELP!! The length of a rectangle is 4 cm more than 3 times its width. If the area of the rectangle is 95 cm2, find the dimensions of the rectangle to the nearest thousandth.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: HELP!! The length of a rectangle is 4 cm more than 3 times its width. If the area of the rectangle is 95 cm2, find the dimensions of the rectangle to the nearest thousandth.       Log On


   

Question 172425: HELP!!
The length of a rectangle is 4 cm more than 3 times its width. If the area of the rectangle is 95 cm2, find the dimensions of the rectangle to the nearest thousandth.



Answer by praseenakos@yahoo.com(507) About Me  (Show Source):
You can put this solution on YOUR website!
Question:
The length of a rectangle is 4 cm more than 3 times its width. If the area of the rectangle is 95 cm2, find the dimensions of the rectangle to the nearest thousandth.
Answer:
Area of a rectangle is given by the formula,
A = length * width
Given, A = +95+cm%5E2
length = 4 cm more than 3 times its width

Let us assume that width = x cm

==> length = 3x + 4 (because, length = 4 cm more than 3 times its width)


so... area = length * width = (3x + 4) * x
95 = (3x + 4) * x
==> 95 = 3x*x + 4* x

==> +95+=+3x%5E2+%2B+4x+


==> +3x%5E2+%2B+4x+-+95+=+0
this is a quadratic equation, you can solve it using quadratic formula
==> x+=+%28-4+%2B-+sqrt%28+%28-4%29%5E2-4%2A3%2A%28-95%29+%29%29%2F%282%2A3%29+
==> x+=+%28-4+%2B-+sqrt%28+16+%2B+1140+%29%29%2F%286%29+
==> x+=+%28-4+%2B-+sqrt%28+1156+%29%29%2F%286%29+

==> x+=+%28-4+%2B-+34%29%2F%286%29+

==> x+=+%28-4+%2B+34%29%2F%286%29+ or x+=+%28-4+-+34%29%2F%286%29+

==> x+=+%2830%29%2F%286%29+ or x+=+%28-38%29%2F%286%29+


==> x+=+5+ or x+=+-6.333+
here u can take the value x= 5 since negative value cant be a length measure

so width = 5 cm

and length = 3*5 + 4 = 15 + 4 = 19


so the dimensions are 19 cm and 5cm

hence the answer.

hope u found it useful.

Regards.

Praseena