a rectangle has a perimeter of 30 inches.Its length is one less than three times its width. what are the length and widths of the rectangle
2(w + 3w-1) = 30
solve for w, and then figure the length
To find the length and width of the rectangle, we can set up a system of equations based on the given information.
Let's assume the width of the rectangle is 'w' inches.
According to the problem, the length of the rectangle is one less than three times its width, which can be expressed as (3w - 1) inches.
The perimeter of a rectangle is given by the formula P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width.
Based on the given information, the perimeter of the rectangle is 30 inches. So, we have the equation:
30 = 2((3w - 1) + w)
Let's solve this equation step by step:
Step 1: Distribute the 2 to the terms inside the parentheses.
30 = 2(3w - 1 + w)
Step 2: Simplify the expression inside the parentheses.
30 = 2(4w - 1)
Step 3: Distribute the 2 to the terms inside again.
30 = 8w - 2
Step 4: Add 2 to both sides of the equation to isolate the variable term.
32 = 8w
Step 5: Divide both sides of the equation by 8 to solve for w.
w = 4
Now, substitute the value of w back into the equation for the length:
l = 3w - 1
l = 3(4) - 1
l = 12 - 1
l = 11
Therefore, the length of the rectangle is 11 inches, and the width is 4 inches.