A brace for a shelf has the shape of a right triangle. Its hypotenuse is 10 inches long and the two legs are equal in length. How long are the legs of the triangle?
This is a classic example of a 45-45-90 triangle: it's a right triangle (one angle of 90) & two other sides of the same length, which means two angles of the same length (and 45 is the only number that will work). With a 45-45-90 triangle, the lengths of the legs are easy to determine: 45-45-90 1-1-sqrt2 Where the hypotenuse corresponds to sqrt2. Now, your hypotenuse is 10. To figure out what each leg is, divide 10/sqrt2 (because sqrt2/sqrt2 = 1, which is a leg length in the explanation above). Problem: you can't divide by radicals. So, we'll have to rationalize the denominator: (10•sqrt2)/(sqrt2•sqrt2) This can be rewritten: 10sqrt2/sqrt(2•2) =10sqrt2/sqrt4 =10sqrt2/2 =5sqrt2
Hope this helps!!
