Question

A right triangle is shown. An altitude is drawn to form a right angle with the opposite side and split the side into lengths of 3 and 3.
What is the value of x?

One-third StartRoot 2 EndRoot units
One-half StartRoot 3 EndRoot units
2 StartRoot 3 EndRoot units
3 StartRoot 2 EndRoot units

Answer 1

Let the hypotenuse be split into 3 and 3, so c = 3 + 3 = 6. For a right triangle with hypotenuse c and adjacent hypotenuse segment p, the corresponding leg a satisfies a^2 = c·p. Thus

a^2 = 6·3 = 18, so a = sqrt(18) = 3√2.

Hence x = 3√2 units.