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.
f 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 leg be L. The hypotenuse is L√2. The altitude to the hypotenuse in a right triangle is (product of the legs)/(hypotenuse) = L^2/(L√2) = L/√2. Set this equal to x: L/√2 = x, so L = x√2.

Answer: x√2 units.