Posted by **aisha** on Wednesday, November 24, 2010 at 8:04am.

the length of a rectangle is 3 less than 5 times its width.

Write a simpified algebriac expression for the perimeter of a rectangle.

If the rectangle width is tripled and its length is doubled,the perimeter of new rectangle is 92cm greater than the original perimeter.

Find the area of the original rectangle.

- maths -
**Reiny**, Wednesday, November 24, 2010 at 8:34am
original width ---> x

original width ---> 5x-3

Perimeter = 2x +2(5x-3) = ....

new width --->3x

new length ---> 2(5x-3)

so 2(3x) + 2(5x-3) = 92

solve for x

....

then evaluate x(5x-3)

let me know what you get.

- maths -
**J**, Wednesday, November 24, 2010 at 8:34am
Hi aisha,

Let's start with formulating an algebriac expression for the perimeter.

We know that perimeter of rectangle = 2(length) + 2(width).

Since we don't know length or width, we let x be the width of the rectangle.

Hence length = 5x-3 [because length = (5 X width) - 3].

So perimeter = 2[5x-3]+2(x) = 10x-6+2x= 12x-6. That answers the first part.

If width is tripled, new width = 3x.

If length is doubled, new length = 2(5x-

3) = 10x-6. So new perimeter = 2(3x)+2(10x-6) = 6x+20x-12= 26x-12.

Now, perimeter of new rectangle - perimeter of original rectangle = 92cm.

So [26x-12]-[12x-6] = 92cm

Simplifying the left hand side, 14x-6=92cm

Therefore, 24x=98cm, x=98/14=7cm.

So to find area of original rectangle, it is length X width = (5x-3)(x) = 5x^2 - 3x = 5(7X7) - 3(7) = 224cm^2

Hope I helped! (:

-J

- maths -
**Reiny**, Wednesday, November 24, 2010 at 8:38am
Go with J's solution, I noticed an error near the end of mine,

my equation should have been

2(3x) + 4(5x-3) = 92

- maths -
**J**, Wednesday, November 24, 2010 at 8:45am
Oops sorry! I realised that I also made a mistake near the end.

When I said "...Therefore, 24x=98cm.." I meant 14x (Not 24!) = 98cm. =)

- maths -
**rooi**, Wednesday, March 14, 2012 at 5:12am
The length of a rectangle is 3cm less than twice the width.The perimeter of the rectangles of the sides of the rectangle is 24cm.Find the lengths of the sides of the rectangle.

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