hypotenuse 4

Question

A brace for a shelf has the shape of a right triangle. Its hypotenuse is
12
inches long and the two legs are equal in length. How long are the legs of the? triangle?

Answer 1

Jessica,

 

Since the two legs have equal length, the triangle is actually isosceles. let x be the length of each leg.

 

By the Pythagorean Theorem,

 

x² + x² = 12²

 

2x² = 144

 

x² = 72

 

x = √72 = 6√2.

 

So, each leg has length 6√2 inches.

 

Its an interesting fact about isosceles right triangles, that is you know one of the legs has length t, the hypotenuse will have length t√2 . Conversely, if the hypotenuse is known to have length h, both legs will have lengths h/√2 .

 

The shortest method of solving this is to use what I just told you. If h = 12, then

 

x = 12/√2 = 12/√2 · √2/√2 = (12√2)/2 = 6√2.  (I rationalized the denominator in the next to last step, though it is hard to see with the way I typed it in.)