a vegetable garden is in the shape of a rectangle, surrounded by 296 feet of fence. the length of the garden is 61 feet more than twice the width of the garden. fins the dimensions of this garden
l (length) = x + 61
w (width) = x
P (perimeter) = 296 ft = 2l ft + 2w ft = 2(x+61) ft + 2x ft = 4x ft + 122 ft
4x = 296 ft - 122 ft = 174 ft
x = 174 ft/4 = 87 ft/2 = 43.5 ft
thus,
l = 43.5 ft + 61 ft = 104.5 ft
and
w = 43.5 ft
ur welcome :)
Why did the rectangle enroll in a fencing competition? Because it wanted to show off its dimensions! Alright, let's solve this puzzle.
Let's assume the width of the garden is 'w' feet. According to the information given, the length of the garden is 61 feet more than twice the width, which can be expressed as 2w+61 feet.
To find the perimeter of the garden, we will add up all the sides of the rectangle:
Perimeter = 2(length + width)
Now we can plug in the values:
296 = 2((2w+61) + w)
Let's simplify the equation:
296 = 2(3w+61)
296 = 6w + 122
6w = 296 - 122
6w = 174
w = 29
So the width of the garden is 29 feet. To find the length, we substitute the value of 'w' into the equation for the length:
Length = 2w + 61
Length = 2(29) + 61
Length = 58 + 61
Length = 119
Therefore, the dimensions of the garden are 29 feet by 119 feet. Happy gardening!
Let:
- Width of the garden be 'w' feet
- Length of the garden be 'l' feet
From the given information, we can create two equations.
1. Perimeter (fence) equation:
The sum of all sides of the rectangle (twice the width + twice the length) is equal to the perimeter of 296 feet.
2w + 2l = 296
2. Relationship between length and width:
The length of the garden is 61 feet more than twice the width.
l = 2w + 61
We can solve these two equations simultaneously to find the dimensions of the garden.
First, let's solve equation 2 for 'l':
l = 2w + 61
Now, substitute this value of 'l' in equation 1:
2w + 2(2w + 61) = 296
2w + 4w + 122 = 296
6w = 296 - 122
6w = 174
w = 174 / 6
w = 29
Now that we know the value of 'w', we can substitute it back in equation 2 to find 'l':
l = 2w + 61
l = 2(29) + 61
l = 58 + 61
l = 119
Therefore, the dimensions of the garden are:
Width = 29 feet
Length = 119 feet
To find the dimensions of the vegetable garden, we can set up a system of equations and solve it using algebra.
Let's assume that the width of the garden is "w" feet. According to the problem, the length of the garden is 61 feet more than twice the width. So, we can represent the length as "2w + 61" feet.
The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width. In this case, we know that the perimeter is 296 feet.
So, we can write the equation as: 296 = 2(2w + 61) + 2w.
Let's simplify and solve for "w":
296 = 4w + 122 + 2w
296 = 6w + 122
subtracting 122 from each side
174=6w
Now, divide both sides by 6 to isolate "w":
174 รท 6 = w
29 = w
Therefore, the width of the garden is 29 feet.
To find the length, substitute the value of the width into the equation for the length:
Length = 2w + 61 = 2(29) + 61 = 58 + 61 = 119
So, the dimensions of the vegetable garden are 29 feet (width) and 119 feet (length).