SOLUTION: A rectangle has a perimeter of 78centimeters. The length of the rectangle is 11 centimeters longer than triple the width. Find the dimensions of the rectangle.

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Question 91543: A rectangle has a perimeter of 78centimeters. The length of the rectangle is 11 centimeters longer than triple the width. Find the dimensions of the rectangle.
Answer by praseenakos@yahoo.com(507) About Me  (Show Source):
You can put this solution on YOUR website!
Question:
A rectangle has a perimeter of 78centimeters. The length of the rectangle is 11 centimeters longer than triple the width. Find the dimensions of the rectangle.

Answer:
Given:

perimeter = 78centimeters



suppose width = x centimeters
tripple the width = 3x
11 centimeter longer than tripple the width = 3x + 11

That is length = (3x + 11 ) centimeters


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

That is:
78 = 2( 3x + 11 + x)

==> 78 = 2(4x +11)
==> 78 = 2* 4x + 2*11

==> 78 = 8x + 22

Subtract 22 from both sides....

==> 78 - 22 = 8x + 22 - 22

==> 56 = 8x

Divide both sides by 8

==> 56%2F8+=+8x%2F8

==> 7 = x

That is width = 7 centimeters.

Then length = 3x + 11 = 3*7 + 11 = 21 + 11 = 32 centimeter.


That is dimensions of the rectangle is;

length = 32 cm and
width = 7 cm

To check your answer, plugg these values in the given formula of perimeter of the rectangle, P = 2(length+width) then you will get the answer 78 centimeters.


Hope you found the explanation useful.

Regards.
Praseena.