SOLUTION: Find the dimensions of a rectangle whose area is 180cm^2 and whose perimeter is 54 cm.

Question 98653: Find the dimensions of a rectangle whose area is 180cm^2 and whose perimeter is 54 cm.
Answer by praseenakos@yahoo.com(507) (Show Source): You can put this solution on YOUR website!
Question:
Find the dimensions of a rectangle whose area is 180cm^2 and whose perimeter is 54 cm.
Answer:
Given that,
and

Perimeter of rectangle is given by the formula, 2( length + width)

==> 2( length + width) = 54

==> ( length + width) =

==> ( length + width) = 27

Now suppose, length = x cm

Then width = 27 - x

Now area is given by the formula, length * width

That is length * width = 180 cm^2

==> x * ( 27-x) = 180

==>

==> -----------------(1)

This is a quadratic equation and you can solve this equation using quadratic formula for x.

==>

Comparing equation(1) with the standard quadratic equation,
, we have,

a = 1, b = -27 and c = 180

==>

==>

==>

==>

==> either, or

==> either, or

==> either, or

that is either length = 15 cm of 12 cm

When length = 15 cm, width = 27 - 15 = 12 cm

And when length = 12cm, width = 27 - 12 = 15 cm.

Hence the solution.

Hope you found the explanation useful.

Regards.

Praseena.

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