The length of a rectangle is twice the width. If the length is increased by 6, and the width is doubled, a new rectangle is formed whose perimeter is 20 more than the perimeter of the original rectangle. Find the dimensions of the original rectangle.
old perimeter is 2(w+2w)
so,
2(2*w+ 2w+6) = 2(w+2w)+20
Now you can find w and 2w.
Length is 8
Width is 4
Let's solve this step by step:
Step 1: Define the dimensions of the original rectangle.
Let's assume the width of the original rectangle is "w" units.
According to the problem, the length of the original rectangle is twice the width. So, the length would be 2w units.
Therefore, the dimensions of the original rectangle are: width = w units, length = 2w units.
Step 2: Define the dimensions of the new rectangle.
To find the dimensions of the new rectangle, we need to make the following modifications to the original rectangle:
- Increase the length by 6 units.
- Double the width.
So, the new length would be 2w + 6 units, and the new width would be 2w units.
Therefore, the dimensions of the new rectangle are: width = 2w units, length = 2w + 6 units.
Step 3: Calculate the perimeters of the original and new rectangles.
The perimeter of a rectangle can be calculated by adding the lengths of all sides.
The perimeter of the original rectangle = 2(length + width)
= 2(2w + w)
= 2(3w)
= 6w
The perimeter of the new rectangle = 2(length + width)
= 2(2w + 6 + 2w)
= 2(4w + 6)
= 8w + 12
Step 4: Set up the equation.
According to the problem, the perimeter of the new rectangle is 20 more than the perimeter of the original rectangle:
(8w + 12) = (6w) + 20
Step 5: Solve the equation.
8w + 12 = 6w + 20
2w = 20 - 12
2w = 8
w = 4
Step 6: Find the dimensions of the original rectangle.
Since we know that the width of the original rectangle is w, which is 4 units, we can find the length of the original rectangle.
Length = 2w = 2(4) = 8
Therefore, the dimensions of the original rectangle are: width = 4 units, length = 8 units.
So, the original rectangle has a width of 4 units and a length of 8 units.