The length of a rectangle is 6 cm more than four times the width. If the perimeter of the rectangle is 42 cm, what are its dimensions?
a. length = 18 cm; width = 3 cm
b. length = 18 cm; width = 9 cm
c. length = 6 cm; width = 9 cm
d. length = 3 cm; width = 18 cm
w = width
4w + 6 = length
P = 2w + 2L
42 = 2w + 2(4w + 6)
Solve for w
To solve this problem, we can set up a system of equations. Let's start by defining the variables:
Let L be the length of the rectangle.
Let W be the width of the rectangle.
We are given two pieces of information:
1. The length of the rectangle is 6 cm more than four times the width. So we can write the equation: L = 4W + 6.
2. The perimeter of the rectangle is 42 cm. The formula for the perimeter of a rectangle is P = 2L + 2W. Substituting the given values, we get: 42 = 2L + 2W.
Now, we can solve this system of equations.
Plug the value of L from the first equation into the second equation:
42 = 2(4W + 6) + 2W.
Simplify the equation:
42 = 8W + 12 + 2W.
Combine like terms:
42 = 10W + 12.
Subtract 12 from both sides:
42 - 12 = 10W.
30 = 10W.
Divide both sides by 10:
30/10 = W.
W = 3.
Now that we have the value of W, we can substitute it back into the equation for L:
L = 4W + 6.
L = 4(3) + 6.
L = 12 + 6.
L = 18.
So the dimensions of the rectangle are:
Length = 18 cm
Width = 3 cm.
Therefore, the correct answer is a) length = 18 cm; width = 3 cm.