the permeter of a rectangle is 148 inches the length exceeds the width by 52 inches find the length and width..
Let w represent the width.
2w + 2(w + 52) = 148
4w + 104 = 148
4w = 44
w = 11
Does that work?
11 + 11 + 63 + 63 = 148
Yep!
yes so the width is 11 and the length is 63
Right. I hope you understand how we get those answers.
To find the length and width 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 x inches. Since the length exceeds the width by 52 inches, the length can be written as (x + 52) inches.
The perimeter of a rectangle is given by the formula:
Perimeter = 2 × (Length + Width)
Substituting the given values into this equation, we have:
148 = 2 × ((x + 52) + x)
To solve this equation and find the values of x (width) and (x + 52) (length), follow these steps:
1. Distribute 2 to the terms inside the parentheses:
148 = 2 × (2x + 52)
2. Simplify the expression:
148 = 4x + 104
3. Subtract 104 from both sides of the equation:
148 - 104 = 4x + 104 - 104
44 = 4x
4. Divide both sides of the equation by 4:
44/4 = 4x/4
11 = x
Now that we have the value of x, we can find the corresponding length (x + 52):
Length = x + 52
Length = 11 + 52
Length = 63
Therefore, the width of the rectangle is 11 inches, and the length is 63 inches.