write a system of equations to represent the situation. Then, solve the system by substitution.

Question

The length of a rectangle is 3 more than it's width. The perimeter of the rectangle is 58cm. What are the rectangle's dimensions? 

Answer 1

Here's what we know:

P = 2L + 2w (perimeter is the two lengths and two widths added together)

L = 3w (length is three times the width)

P = 58 (the perimeter of this particular rectangle is 58 cm)

 

Since we have values for our variables, let's plug them in:

58 = 2(3w) + 2w

Distribute that 2:

58 = 6w + 2w

Simplify:

58 = 8w

Isolate by dividing both sides by 8:

7.25 = w

 

Now that we know w, we can solve for L:

L = 3 * 7.25

L = 21.75

 

Check:

58 = 2 * 21.75 + 2 * 7.25

58 = 43.5 + 14.5

58 = 58