brace for a shelf 6

Question

A brace for a shelf has the shape of a right triangle. Its hypotenuse is
22
inches long and the two legs are equal in length. How long are the legs of the? triangle?


The legs of the triangle are both
______inches long.

Answer 1

 

Since the 2 legs are equal in length, that means the angles opposite those sides are congruent.

The 2 angles are 45 degrees.  This is a special right triangle ... 45º-45º-90º

 

The side ratios are x:x:x√2

 

It is given that the hypotenuse is 22.

 

Thus, 22 = x√2

 

Solving for x,

 

    22/√2 = (x√2)/√2

    22/√2 = x

 

Rationalizing the denominator,

 

       22√2/2 = x

       11√2 = x

 

Each leg is 11√2,  approximately 15.56