The length of a rectangle is 10 feet more than twice its width. The perimeter of
the rectangle is 170 feet. Find the dimensions of the rectangle.
let the width be x feet, then the length is 2x+10 feet
2(x) + 2(2x+10) = 170
6x + 20 = 170
x = 25
so the width is 25 feet and the length is 60 feet
check: is 2(25) + 2(60) = 170 ? Yes!
To find the dimensions of the rectangle, we need to set up an equation based on the given information.
Let's assume that the width of the rectangle is "w" feet.
According to the problem, the length of the rectangle is "10 feet more than twice its width." So, the length can be expressed as: 2w + 10.
The perimeter of a rectangle is the sum of all its sides. In this case, the perimeter is given as 170 feet. For a rectangle, the perimeter is calculated as: 2(l + w), where l is the length and w is the width.
Using the above formula, we can set up an equation:
2(2w + 10 + w) = 170
Now, let's solve the equation to find the value of "w":
4w + 20 + 2w = 170
6w + 20 = 170
6w = 170 - 20
6w = 150
w = 150 / 6
w = 25
So, the width of the rectangle is 25 feet.
Now, we can find the length:
Length = 2w + 10
Length = 2(25) + 10
Length = 50 + 10
Length = 60
Therefore, the dimensions of the rectangle are:
Width = 25 feet
Length = 60 feet