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.
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! (:
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
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.
basic geometric - 10. a rectangle has width the same as a side of a square whose...
Math - The variable W represents the width of a rectangle. The length of the ...
basic geometry - A rectangle has width the same asa a side of a square whose ...
geometry - If the length of a rectangle is twice its width, w, write an ...
math - the length of a rectangle is 5 ft more than twice the width. a)if x ...
algebra - The length of a rectangle is 5 inches longer than its width. Its ...
9th grade polynomials - How do you write the expression for the area of the ...
algebra , help - Can someone help me set up the equations thanks. Directions: ...
math117 - The area of a rectangle of length x is given by 3x2 +5x. Find the ...
math - The length, l, of a rectangle is 2 feet less than three times the width, ...