The length of a rectangle is four more than five times its width. Its perimeter is 92 inches. Find its dimensions length and width.
P = 2L + 2W
92 = 2(5W + 4) + 2W
92 = 12W + 8
84 = 12W
? = W
Let's break this down step-by-step to find the dimensions of the rectangle:
Step 1: Assign variables:
Let's assume that the width of the rectangle is 'w' inches.
So, the length of the rectangle would be '5w + 4' inches.
Step 2: Perimeter of a rectangle:
The perimeter of a rectangle is given by the formula: P = 2(l + w)
Given that the perimeter is 92 inches, we can write the equation as:
92 = 2(5w + 4 + w)
Step 3: Simplify the equation:
Expand the equation:
92 = 2(6w + 4)
Step 4: Distribute the 2 on the right side:
92 = 12w + 8
Step 5: Move 8 to the left side:
92 - 8 = 12w
84 = 12w
Step 6: Divide both sides by 12:
84/12 = w
7 = w
Step 7: Finding the length:
Using the value of 'w' we found, substitute it back into the equation for length:
Length = 5w + 4
Length = 5(7) + 4
Length = 35 + 4
Length = 39
So, the width of the rectangle is 7 inches, and the length is 39 inches.
To find the dimensions of the rectangle, we need to set up a system of equations using the given information.
Let's denote the width of the rectangle as "w" and the length as "l".
From the given information, we know that the length of the rectangle is four more than five times its width:
l = 5w + 4 ...(Equation 1)
We also know that the perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)
Given that the perimeter is 92 inches, we can substitute the values into the formula:
92 = 2(l + w) ...(Equation 2)
Now, we have two equations (Equation 1 and Equation 2) with two variables (l and w). We can solve this system of equations to find the values of l and w.
Step 1: Solve Equation 1 for l in terms of w:
l = 5w + 4
Step 2: Substitute the value of l from Step 1 into Equation 2:
92 = 2((5w + 4) + w)
Step 3: Simplify and solve for w:
92 = 2(6w + 4)
46 = 6w + 4
42 = 6w
w = 7
Step 4: Substitute the value of w back into Equation 1 to find l:
l = 5(7) + 4
l = 35 + 4
l = 39
So, the width of the rectangle is 7 inches and the length is 39 inches.