A rectangle's length is 3 cm less than twice it's width. if the length is decreased by 2 cm and the width is decreased by 1 cm, the perimeter will be 24 cm. find the dimensions of the original rectangle.
w=10
width: w
length: 2w-3
after the changes, we have
(2w-3-2 + w-1) = 24
Now just solve for w, the original width.
The length of a rectangle is 3 cm less than twice its width. If the length is decreased by 2 cm and the width is decreased by 1 cm, the perimeter will be 24 cm. find the dimensions of the original rectangle.
Find X, 'find equation, and find answer plz.
To find the dimensions of the original rectangle, let's define the variables:
Let the width of the rectangle be 'w' cm.
Then, the length of the rectangle is 2w - 3 cm. (length = 3 cm less than twice the width)
Now, let's use the given information to create an equation:
When the length is decreased by 2 cm and the width is decreased by 1 cm, the perimeter will be 24 cm.
The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
So, we have:
2((2w - 3) - 2 + (w - 1)) = 24
Let's simplify and solve this equation:
2(2w - 5 + w - 1) = 24
2(3w - 6) = 24
6w - 12 = 24
6w = 24 + 12
6w = 36
w = 36 / 6
w = 6
Now we have the width of the rectangle, which is 6 cm.
To find the length, we substitute the value of w into the original equation:
Length = 2w - 3
Length = 2(6) - 3
Length = 12 - 3
Length = 9
Therefore, the dimensions of the original rectangle are:
Width = 6 cm
Length = 9 cm