The hypotenuse of a right triangle is

Adam Lyons, Magoosh Tutor

Hey Varun,

Since this is a data sufficiency question, we shouldn't worry about solving. The bottom line is that we have two equations and two unknowns, which is always solvable:

b² + h² = 10²
0.5bh = 25

In any case, we want b + h. If you square b + h, you get:

b² + 2bh + h²

And we know these values:

(b² + h²) + 2bh = 100 + 100 = 200

Hence:

(b + h)² = 200

b + h = √200

And the perimeter, then, is 10 + √200.

Sep 24, 2019 • Reply