Question

The length of a rectangle is 6cm less than 4 times its width. find the dimensions of the rectangle if its perimeter is 48 cm

Answer 1

Let's look at the formula to find the perimeter.
2l+2w=48
We know that the length is 6 less than 4 times the width, so the equation would be: L=4w-6; let's plug it in.
2(4w-6)+2w=48
8w-12+2w
10w-12=48
10w=60
60÷10=6=w
So the width is 6. If L=4w-6, we can figure out the length using this equation.
4(6)-6
24-6=18
So, the length is 18 cm while the width is 6 cm.
Tell me if this helps!!

Answer 2

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

Let's identify our values:

X → Width

4x - 6 → length

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

Now, we can use the second sentence to set up our equation. The perimeter of the rectangle is the distance around the outside of the figure. Let's set up our equation.

x + x + 4x - 6 + 4x - 6 = 48

We can simplify on the left and our equation will now read

10x - 12 = 48

+12 +12

10x =60

÷10 ÷10

X = 6

Width = 6 cm

Length = 18 cm