Question

A right triangle is shown. An altitude is drawn to form a right angle with the opposite side. The length of the altitude is x. The other 2 sides are congruent.
If the altitude of an isosceles right triangle has a length of x units, what is the length of one leg of the large right triangle in terms of x?

x units
xStartRoot 2 EndRoot units
xStartRoot 2 EndRoot units
2x units

Answer 1

Let each congruent leg be L. In a 45-45-90 triangle the hypotenuse is L√2, and the altitude to the hypotenuse has length (product of legs)/(hypotenuse) = L^2/(L√2)=L/√2.
So x = L/√2, hence L = x√2.

Answer: x√2 units.