Question

The length of a rectangle is three times the width. the perimeter is 44 cm what are the dimension of the rectangle

Answer 1

We know that the perimeter is 44, and perimeter is 2l + 2w.
2l + 2w = 44

We also know that the length, which I will call l, is three times the width, which I will call w.d
l = 3w

Let's rearrange this so it matches the first equation.
l - 3w = 0

Now we can set up a system of equations:
2l + 2w = 44
l - 3w = 0

Multiply the second equation by -2 so we can get the l's to cancel

2l + 2w = 44
-2l + 6w = 0

Now add them together and solve for w.
8w = 44
w = 5.5

Knowing w, we can solve for l using either original equation.
l = 3w
∴ l = 3(5.5)
   l = 16.5

To check this, we can substitute the numbers back into the original equation:
2(16.5) + 2(5.5) = 44 
16.5 = 3(5.5)

So the dimensions of the rectangle are 16.5 x 5.5
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