The perimeter of a rectangle is 42 feet and its length is 3 feet less than 5 times its width find the dimensions of rectengle through linear equation.
The perimeter of a garden is 42 feet. The length is 15 feet. what is the width?
To solve this problem, let's set up an equation using the given information.
Let's assume the width of the rectangle is "W" feet.
According to the given information, the length of the rectangle is 3 feet less than 5 times its width. So the length can be represented as (5W - 3) feet.
The formula for the perimeter of a rectangle is: P = 2(length + width)
In our case, the perimeter is given as 42 feet. So we can set up the equation as:
42 = 2((5W - 3) + W)
Let's simplify the equation step by step:
42 = 2(6W - 3)
42 = 12W - 6
Now, let's isolate the W term by bringing -6 to the other side:
12W = 42 + 6
12W = 48
Finally, divide both sides of the equation by 12 to solve for W:
W = 48 / 12
W = 4
So the width of the rectangle is 4 feet.
Now, let's substitute the value of W back into the expression for the length to find the length of the rectangle:
Length = 5W - 3
Length = 5(4) - 3
Length = 20 - 3
Length = 17
So the length of the rectangle is 17 feet.
Therefore, the dimensions of the rectangle are: Width = 4 feet and Length = 17 feet.
To find the dimensions of a rectangle using a linear equation, we can start by assigning variables to the unknown values.
Let's denote the width of the rectangle as "w" and its length as "l".
We know that the length is 3 feet less than 5 times the width, so we can write the equation:
l = 5w - 3
The perimeter of a rectangle is calculated by adding all four sides together. For this rectangle, we add the length twice and the width twice:
Perimeter = 2l + 2w
Given that the perimeter is 42 feet, we can write the equation:
42 = 2l + 2w
Now we can substitute the expression for "l" into the equation:
42 = 2(5w - 3) + 2w
Simplifying:
42 = 10w - 6 + 2w
Combining like terms:
42 = 12w - 6
Adding 6 to both sides:
48 = 12w
Dividing both sides by 12:
4 = w
Therefore, the width of the rectangle is 4 feet.
To find the length, we can substitute this value back into the equation for "l":
l = 5w - 3
l = 5(4) - 3
l = 20 - 3
l = 17
Therefore, the length of the rectangle is 17 feet.
The dimensions of the rectangle are: width = 4 feet and length = 17 feet.
W = width
Length = 5 times width - 3 ft
= 5W-3
Perimeter, 42 ft = 2 (Length+Width)
=2( 5W-3 + W)
Therefore
2(5W-3 + W) = 42
solve for W.