SOLUTION: A right angled triangle has one leg of 12 cm and a hypotenuse of 14 cm. Find the length of the third side.

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Question 974285: A right angled triangle has one leg of 12 cm and a hypotenuse of 14 cm. Find the length of the third side.
Answer by farohw(175) About Me  (Show Source):
You can put this solution on YOUR website!

Assuming one leg is (a) and the hypotenuse is (c),the formula we will use for a right-angled triangle is:

b+=+sqrt%28c%5E2+-+a%5E2%29 where b is the length of the third side.

We plug the values into the equation,

+b+=+sqrt%2814%5E2+-+12%5E2%29

The length of the third side is b+=+2sqrt%2813%29 or b ~ 7.21 cm.

To show how you obtained the answer b+=+2sqrt%2813%29:

b = sqrt%2814%5E2+-+12%5E2%29+=+sqrt%28196+-+144%29+=+sqrt%2852%29

We separate sqrt%2852%29 as sqrt%284+%2A+13%29 ---> sqrt%284%29+%2A+sqrt%2813%29 since 4 x 13 = 52.

We know that sqrt%284%29+=+2 and sqrt%2813%29 cannot be simplified so we keep it and,

b = 2sqrt%2813%29 or b ~ 7.21cm.