The length of a rectangle is 3 times the width. If the length is increased by 4 cm and the width is decreased by 1 cm,the parimeter would be 102 cm, find the dimensions of the original rectangle.
the permeter of a rectangle is 90cm what is the area of the rectangle if the width is (2x+6) and the length is (3x-1)
2((3w+4)+(w-1)) = 102
w=12
2((2x+6)+(3x-1))) = 90
x=8
So, on both problems, you can now figure the answers needed.
To solve this problem, we can set up a system of equations using the given information:
Let's say the width of the original rectangle is "w" cm.
According to the given information, the length of the rectangle is 3 times the width, so the length would be 3w cm.
After the length is increased by 4 cm, it would become (3w + 4) cm.
Similarly, after the width is decreased by 1 cm, it would become (w - 1) cm.
The formula for the perimeter of a rectangle is P = 2L + 2W, where P represents the perimeter, L is the length, and W is the width.
Now, we can set up the equation based on the given information:
2(3w + 4) + 2(w - 1) = 102
Simplifying the equation gives us:
6w + 8 + 2w - 2 = 102
8w + 6 = 102
8w = 96
Dividing both sides by 8, we find that w = 12.
To find the length of the original rectangle, we can substitute the value of w into the equation we defined earlier:
Length = 3w = 3(12) = 36
Therefore, the dimensions of the original rectangle are 12 cm for the width and 36 cm for the length.