Question

The lengths of the four sides of a quadrilateral (in feet) are consecutive integers. If the

perimeter is 66 feet, find the value of the longest of the four side lengths.

Answer 1

18 feet

Explanation:

We don't know any of the sides of this four-sided shape. "Quadrilateral" means the shape has four sides.

Let's let the smallest side be x.

"Consecutive integers" means that the answers are whole numbers and they are all in a row, in order. Like 2,3,4,and5. But that only adds up to 14. We need to find the ones that add up to 66. The perimeter is all the sides added together.

If the smallest one is x, then the next bigger side is x+1. The next bigger after that is x+2 and the biggest side is x+3.

Add up all the sides to equal 66.

x+x+1+x+2+x+3=66

Combine like terms.

4x + 6 = 66

Subtract 6 from both sides.

4x = 60

Divide by 4.

x = 15.

x = 15 is the smallest side. The biggest side is x+3. That is what we were asked for.

x+3 = 15 + 3

= 18

The biggest side is 18 feet.