One side of a kite is 2 cm less than 5 times the length of another. If the permiter is 32cm find the lenght of each side of the kite.

Expert Answers
bridgetrbcs eNotes educator| Certified Educator

First step would be to draw a kite on your paper.  Remember that perimeter means the distance AROUND a shape so you would need to add up all of the sides to get the perimeter. 

If one side is 2 cm less than 5 times the length of the other side, we can label the "other side" (let's make it one of the smaller sides at the top) X.  Both of the top small sides are congruent so they are both x.  Also, both of the longer bottom sides are both congruent as well.  Remember that congruent means equal in measure.

The longer bottom sides are 2cm less than 5 times the length of the other side, which is x. 

  • 2cm less than means minus 2.
  • 5 times the length of the other side means 5x
  • put them together and we have 5x-2

Thus far we know that the sides are x, x, 5x-2, and 5x-2 for the four sides of the kite.  To get perimeter, we would have to add them up to the total given of 32.

  • x + x + 5x-2 + 5x - 2 = 32
  • 12x - 4 =32 (Combine like terms.)
  • 12x = 36 (add 4 to both sides)
  • x = 3 (divide by 12)

If x = 3, then the two shorter top sides of our kite are 3 cm each.  Remember that the longer sides are 5x-2.  Place the 3 in place of x.

5(3) - 2

15-2

13

The longer sides are 13 cm long. 

Hope this helps you!