What is the length of the longer side in this triangle

Did you notice the little box with corners marked in the angle down at the bottom ?
That angle is a right angle, and this triangle is a right triangle !

This piece of information is a big help.  It breaks the problem wide open.
You know that in order to find the longest side of a right triangle . . .

-- Square the length of one short side.
-- Square the length of the other short side.
-- Add the two squares together.
-- Take the square root of the sum.

One short side=48.           Its square = 2,304.
The other short side=48.  Its square = 2,304.
Add the two squares:        2,304 + 2,304 = 4,608

The square root of the sum = √4,608 = 67.88 (rounded)