The length of a rectangle is 2 cm more than four times the width. If the perimeter of the rectangle is 84 cm, what are its dimensions?
P = 2L + 2W
84 = 2(4W + 2) + 2W
84 = 8W + 4 + 2W
80 = 10W
8 = W
Let's solve this step by step:
Step 1: Let's assume that the width of the rectangle is "w" cm.
Step 2: We are given that the length of the rectangle is 2 cm more than four times the width. Therefore, the length can be represented as "4w + 2" cm.
Step 3: The perimeter of a rectangle is given by the formula: P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width.
Step 4: Substituting the given values, the perimeter of the rectangle is 84 cm. Therefore, we can write the equation as: 84 = 2(4w + 2 + w).
Step 5: Simplifying the equation, we get: 84 = 2(5w + 2).
Step 6: Distributing the multiplication, we get: 84 = 10w + 4.
Step 7: Subtracting 4 from both sides, we get: 80 = 10w.
Step 8: Dividing by 10 on both sides, we get: 8 = w.
Step 9: Now that we have the value of the width, we can substitute it back into the equation for the length. Therefore, the length of the rectangle is: 4w + 2 = 4(8) + 2 = 32 + 2 = 34 cm.
Step 10: The dimensions of the rectangle are: Width = 8 cm, Length = 34 cm.
Therefore, the dimensions of the rectangle are 8 cm (width) and 34 cm (length).
To find the dimensions of the rectangle, we can set up equations based on the given information.
Let's assume the width of the rectangle is "w" cm.
According to the problem, the length of the rectangle is 2 cm more than four times the width. So, the length can be expressed as (4w + 2) cm.
The formula for the perimeter of a rectangle is given by P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width.
In this case, the perimeter is given as 84 cm. So, we can write the equation as 84 = 2(4w + 2 + w).
Solving this equation will give us the value of w, which we can then use to find the length of the rectangle.
Let's solve the equation step by step:
84 = 2(4w + 2 + w)
84 = 2(5w + 2)
84 = 10w + 4
80 = 10w
w = 8
Now that we have the width, we can substitute it back into the equation for the length to find its value:
l = 4w + 2
l = 4(8) + 2
l = 32 + 2
l = 34
Therefore, the dimensions of the rectangle are 8 cm (width) and 34 cm (length).