The numbers are consecutve, the perimeter is 162, how long is each sides of the qiadrilateral?

Question

Perimeter is 162, how long is each sides of the quadrilateral

Answer 1

The numbers are consecutive, which means one number is one more than the other; length equals width plus 1:

 

l = w + 1

 

Perimeter is two times the length plus two times the width:

 

P = 2l + 2w.

 

Using substitution, substitute the expression for l from into the perimeter equation:

 

P = 2(w+1) + 2w 

 

Set the perimeter equal to 162 (given in the problem): and solve for the width:

 

162 = 2(w+1) + 2w

 

and then use the result for the width to solve for the length:

 

l = w +1

 

Try it!

 

 

Answer 2

Let x = the shortest side

Let x + 1 = the next second side

Let x + 2 = the third side

Let x + 3 = the longest side

x + x + 1 + x + 2 + x + 3 = 162

4x + 6 = 162

4x = 156

x = 39

x + 1 = 40

x + 2 = 41

x + 3 = 42