The width of a rectangle is 3 yards less than its length. the perimeter is 130 yards. Find the length and width of the rectangle
P = 2L + 2W
W = L - 3
P = 2L + 2(L - 3)
130 = 4L - 6
136 = 4L
34 = L
W = 31
width --- x
length --- x-3
solve
2x + 2(x-3) = 130
Let's solve the problem step by step.
Step 1: Set up the equations.
Let L be the length of the rectangle.
Since the width is 3 yards less than the length, the width would be L - 3.
Step 2: Use the formula for the perimeter of a rectangle.
The perimeter of a rectangle is given by the formula: P = 2*(Length + Width).
In this case, P = 130, so we can write the equation:
130 = 2*(L + L - 3).
Simplify the equation:
130 = 2*(2L - 3).
Step 3: Solve the equation.
Distribute the 2 on the right side of the equation:
130 = 4L - 6.
Add 6 to both sides of the equation:
130 + 6 = 4L - 6 + 6.
136 = 4L.
Divide both sides by 4 to isolate L:
136/4 = 4L/4.
34 = L.
So, the length of the rectangle is 34 yards.
Step 4: Find the width.
The width is 3 yards less than the length, so substituting L with 34 in the equation for the width:
Width = L - 3 = 34 - 3 = 31 yards.
Therefore, the length of the rectangle is 34 yards and the width is 31 yards.
To find the length and width of the rectangle, we can set up a system of equations based on the given information.
Let's represent the length of the rectangle as 'L' and the width as 'W'.
From the given information, we know that the width is 3 yards less than the length. So, we can write the first equation as:
W = L - 3
We also know that the perimeter of a rectangle is given by the formula: P = 2L + 2W.
According to the problem, the perimeter is 130 yards, so we can write the second equation as:
130 = 2L + 2W
Now that we have the system of equations, we can solve it to find the values of L and W.
Substitute the value of W from the first equation into the second equation:
130 = 2L + 2(L - 3)
Simplify the equation:
130 = 2L + 2L - 6
Combine like terms:
130 = 4L - 6
Add 6 to both sides:
130 + 6 = 4L
136 = 4L
Divide both sides by 4:
136/4 = L
34 = L
Now that we have the value of L, we can substitute it back into the first equation to find W:
W = L - 3
W = 34 - 3
W = 31
Therefore, the length of the rectangle is 34 yards and the width is 31 yards.