Triangle problems

Question

A right triangle has angles which measure 30,60 and 90 degrees.

If the perimeter of this triangle is 15+5*3^(1÷2). Then the length of the hypotenuse of this triangle is= ?

Answer 1

the answer is

Answer 2

Remember that the side ratios for a 30-60-90 degree right triangle are x, 2x, x√3.

Since your perimeter is 15 + 5√3, x must be 5 because the 15 and the 5√3 could not be combined.  That means that the hypotenuse is 2x, and since x=5 the hypotenuse is 10.