Question 91543
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


==> {{{56/8 = 8x/8}}}


==> 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.