Question

the perimeter of a rectangle is 124 cm. the length is six more than three times the width. what are the dimensions of the rectangle?

Answer 1

P = 2(L + W)
P = 124
L = 3W + 6

124 = 2(3W + 6 + W)
124 = 2(4W + 6)
124 = 8W + 12
124 - 12 = 8W
112 = 8W
112/8 = W
14 = W <=== width is 14 cm

L = 3W + 6
L = 3(14) + 6
L = 42 + 6
L = 48 <=== length is 48 cm

Answer 2

Our first task in this problem is to set up variables that represent length and width.

Let's first identify our values:

X → Width

3x + 6 → Length

Before moving on, it's always a great idea to draw a picture of the rectangle to visualize what's going on. I will provide a picture.

Now, we can use the first sentence of the problem to set up our equation.

The perimeter of a rectangle is the distance around the outside of the figure. If our perimeter is 124 cm, we can set up an equation to represent this.

x + x + 3x + 6 + 3x + 6 = 124cm.

If we simplify on the left side we will get

8x + 12 = 124

      -12    -12

8x = 112

÷8    ÷8

X = 14

Width = 11 cm

Length = 48 cm