The length of a rectangle is 3 times the width. If the length is increased by 4 cm and the width is decreased by 1cm the parimeter will be 102 cm. find the dimensions of the original rectangle.
I don't know the equation, please show the work. Not just the answer. So I can learn how to do this.
Thanks.
you know the perimeter is
2(width + length)
So, now you are told that l = 3w and that
2((l+4)+(w-1)) = 102
since l=3w, that means
2((3w+4)+(w-1)) = 102
3w+4+w-1 = 51
4w+3 = 51
4w = 48
w = 12
Now you can figure the original length.
the real problem, as I see it, is that you don't know the formula. How can you be given a problem about perimeters and not have learned how the perimeter is figured?
To solve this problem, let's assign variables to the unknown quantities. Let's say the width of the rectangle is "w" cm. According to the problem, the length of the rectangle is 3 times the width, so the length is "3w" cm.
The perimeter of a rectangle is calculated by adding up the lengths of all four sides. In this case, the perimeter is given as 102 cm. So we can write the equation:
2(length + width) = perimeter
Substituting the given values, we have:
2(3w + w) = 102
Now, let's solve this equation step by step:
1. Distributing the 2 on the left side:
6w + 2w = 102
Combining like terms:
8w = 102
Dividing both sides by 8 to solve for w:
w = 102/8
w = 12.75
So, the width of the rectangle is 12.75 cm.
Since the length is 3 times the width, the length is:
3w = 3 * 12.75
length = 38.25 cm
Therefore, the dimensions of the original rectangle are:
Width = 12.75 cm
Length = 38.25 cm