maths
posted by aisha on .
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.

original width > x
original width > 5x3
Perimeter = 2x +2(5x3) = ....
new width >3x
new length > 2(5x3)
so 2(3x) + 2(5x3) = 92
solve for x
....
then evaluate x(5x3)
let me know what you get. 
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 = 5x3 [because length = (5 X width)  3].
So perimeter = 2[5x3]+2(x) = 10x6+2x= 12x6. That answers the first part.
If width is tripled, new width = 3x.
If length is doubled, new length = 2(5x
3) = 10x6. So new perimeter = 2(3x)+2(10x6) = 6x+20x12= 26x12.
Now, perimeter of new rectangle  perimeter of original rectangle = 92cm.
So [26x12][12x6] = 92cm
Simplifying the left hand side, 14x6=92cm
Therefore, 24x=98cm, x=98/14=7cm.
So to find area of original rectangle, it is length X width = (5x3)(x) = 5x^2  3x = 5(7X7)  3(7) = 224cm^2
Hope I helped! (:
J 
Go with J's solution, I noticed an error near the end of mine,
my equation should have been
2(3x) + 4(5x3) = 92 
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. =) 
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.

In a given rectangle,the length is two less than four times the width,w.Find the expression that represents the area and the perimeter.