The length of a rectangle is 2 inches more than twice its width. If the perimeter of the rectangle is 34 inches, find the dimensions of the rectangle
w = width
l = length
p = perimeter
p = 2w + 2(2w + 2)
34 = 2w + 4w + 4 - distributive property
34 = 6w + 4
30 = 6w - move the 4 to the other side
30/6 = 6w/6
5 = w
to check that
w + w + (2w + 2) + (2w + 2)
5 + 5 + (2(5)+ 2) + (2(5)+ 2)
10 + 12 + 12
=34
call width w
then length = (w+2)
perimeter = 2 w + 2(w+2)
I think you can get it from there
To find the dimensions of the rectangle, we can set up a system of equations using the given information.
Let's denote the width of the rectangle as w inches.
According to the problem, the length of the rectangle is 2 inches more than twice its width, which can be expressed as: length = 2w + 2 inches.
The formula for the perimeter of a rectangle is: perimeter = 2(length + width)
Substituting in the known values, we have: 34 = 2(2w + 2 + w)
Simplifying the equation, we get: 34 = 2(3w + 2)
Now, let's solve for w:
34 = 6w + 4
30 = 6w
w = 5
Therefore, the width of the rectangle is 5 inches.
To find the length, we can substitute the value of w back into the equation for the length:
Length = 2w + 2
Length = 2(5) + 2
Length = 10 + 2
Length = 12
Therefore, the length of the rectangle is 12 inches.
The dimensions of the rectangle are 5 inches (width) by 12 inches (length).
To find the dimensions of the rectangle, let's assign variables to the width and length of the rectangle.
Let's say the width of the rectangle is 'w' inches. According to the given information, the length of the rectangle is "2 inches more than twice its width," which can be written as 2w + 2.
The perimeter of a rectangle is found by adding up all four sides, which for a rectangle is equal to 2 times the sum of its width and length. In this case, the perimeter is given as 34 inches. So we can set up the equation:
2(w + (2w + 2)) = 34
Let's solve this equation step by step:
2(w + 2w + 2) = 34
2(3w + 2) = 34
6w + 4 = 34
Subtract 4 from both sides:
6w = 30
Divide both sides by 6:
w = 5
Now that we have the width 'w', we can substitute it back into the expression we found for the length:
Length = 2w + 2
= 2(5) + 2
= 10 + 2
= 12
So, the dimensions of the rectangle are a width of 5 inches and a length of 12 inches.