SOLUTION: If a square has a perimeter of 24 inches, how many inches long is its diagonal?

Algebra ->  Pythagorean-theorem -> SOLUTION: If a square has a perimeter of 24 inches, how many inches long is its diagonal?      Log On


   

Question 332131: If a square has a perimeter of 24 inches, how many inches long is its diagonal?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
If a square has a 24-inch perimeter, then the length of one side must be 24%2F4+=+6inches.
Two adjacent sides and the diagonal form a right triangle, so you can find the length of the diagonal using the Pythagorean theorem.
Let the diagonal = c, then:
c%5E2+=+a%5E2%2Bb%5E2 where a and b are two of the sides each 6 inches long.
c%5E2+=+6%5E2%2B6%5E2
c%5E2+=+72 Take the square root of both sides.
c+=+sqrt%2872%29
c+=+8.49 inches, to the nearest hundredth.