Question

What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 9 and 5?

Answer 1

hypotenuse `=sqrt(106) ~= 10.3`

Explanation:

By the Pythagorean Theorem for a triangle with sides `a, b, c` where `c` is the hypotenuse:
`color(white)("XXX")c^2=a^2+b^2`
`rArr`
`color(white)("XXX")c=sqrt(a^2+b^2)`

Substituting `a=9` and `b=5`
we have
`color(white)("XXX")c=sqrt(9^2+5^2) =sqrt(81+25) =sqrt(106)`

(A calculator may be used to evaluate `sqrt(106)` as approximately `10.3`)