Question

The lengths of two sides of a right triangle are 24 meters and 25 meters. Determine the two possible measures for the third side? Possible side length , possible side length Write answer in form numbersqrt(number) or sqrt(number) or number

Answer 1

`7 or sqrt{1201}`

Explanation:

The other side is either the hypotenuse or one of the perpendicular sides.

`c^2 = a^2 + b^2`

As hypotenuse, we're given `a,b,` and solve for `c`.

`c^2 = 24^2 + 25^2 = 1201`

`c = sqrt{1201}`

As a side, we're given the hypotenuse and the other side:

`25 ^2 = 24^2 + b^2`

`b^2 = 25^2 - 24^2 = (25+24)(25 - 24) = 49`

`b = 7`

A Pythagorean Triple: `7^2 + 24^2 = 25^2`

Answer 2

possible third sides are 7 & `sqrt(1201)`

Explanation:

by using Pythagoras theorem,(if 25 is hypotenuse.)
`sqrt(25^2-24^2)`
=`sqrt(625-576)`
=`sqrt(49)`
=7

OR
(if unknown side is hypotenuse.)
`sqrt(25^2+24^2)`
=`sqrt(625+576)`
=`sqrt(1201)`