a rectangle has a length that is four more than three times the width. If the perimeter is 126 feet, find the length and the width
L = 3W+4
2(L+W) = 126
2(3W+4 + W) = 126
2(4W+4) = 126
8(W+1) = 126
W+1 = 15.75
W = 14.75
L = 3W+4 = 48.25
2(14.75+48.25) = 2(63) = 126
A garden is shaped like a rectangle whose perimeter is 300 ft. The length is 9 times as long as the width. Find the length and the width.
Let's denote the width of the rectangle as "w".
According to the given information, the length of the rectangle is four more than three times the width. So, the length can be expressed as 3w + 4.
The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
We know that the perimeter of the rectangle is 126 feet, so we can set up the equation:
2(3w + 4) + 2w = 126
Now, let's solve this equation step-by-step to find the width (w) and the length (3w + 4).
Step 1: Distribute the 2 to each term inside the parentheses:
6w + 8 + 2w = 126
Step 2: Combine like terms on the left side of the equation:
8w + 8 = 126
Step 3: Subtract 8 from both sides of the equation:
8w = 126 - 8
8w = 118
Step 4: Divide both sides of the equation by 8:
w = 118 / 8
w = 14.75
So, the width of the rectangle is 14.75 feet.
Step 5: Now, substitute the value of w back into the equation for the length:
l = 3w + 4
l = 3(14.75) + 4
l = 44.25 + 4
l = 48.25
Therefore, the length of the rectangle is 48.25 feet.
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 that the width of the rectangle is represented by 'w' feet. According to the problem, the length is four more than three times the width, which can be represented as '3w + 4' feet.
The perimeter of a rectangle is given by the formula: 2 * (length + width). Using this, we can set up our equation:
2 * (3w + 4 + w) = 126
Now, let's solve the equation step-by-step:
First, simplify the equation by combining like terms:
2 * (4w + 4) = 126
Next, distribute the 2:
8w + 8 = 126
Then, isolate the variable by subtracting 8 from both sides:
8w = 118
Finally, divide both sides by 8 to solve for 'w':
w = 118 / 8
w ≈ 14.75
So, the width of the rectangle is approximately 14.75 feet.
To find the length, we substitute this value back into the expression '3w + 4':
Length = 3w + 4 = 3(14.75) + 4 ≈ 44.25 + 4 ≈ 48.25
Therefore, the length of the rectangle is approximately 48.25 feet.