The length of a rectangle is 5 cm more than twice the width. The perimeter of the rectangle is 34 cm. Find the dimensions of the rectangle.

Question

I am having trouble with this problem. I asked my parents and they didnt know what to do. I am stuck and i have looked through my notes and nothing has helped. 

Answer 1

The dimensions of the rectangle are two unknowns: The length "l" and the width "w"

 

The perimeter of a rectangle is found as P = 2*l + 2*w

 

We also know that the length is 5cm more than twice the width. l = 2*w + 5

 

These two equations gives us a system of linear equations.

 

P = 2*l + 2*w

l = 2*w + 5

 

We can use substitution to replace the "l" in the first equation with 2*w + 5

 

P = 2*(2*w + 5) + 2*w

P = 4*w + 10 + 2*w

P = 6*w + 10

 

We know that P = 34cm

 

34 = 6*w + 10

 

Subtract 10 from both sides

24 = 6 * w

 

Divide both sides by 6

4 = w

 

Now that we know the width, we can find the length by substituting 4 for "w" in the second equation.

 

l = 2*4 + 5

l = 8 + 5

l = 13

 

The dimensions of the rectangle is 13cm x 4cm