Question

15.

Answer 1

Answer:

13

Step-by-step explanation:

Let PS = x and RP = x-5

Using Pythagorean theorem on the two smaller rt triangles formed,

6^2 + x^2 = (ST)^2

6^2 + (x-5)^2 = (RT)^2

Now use Pythag on big triangle and sub in above values:

(2x-5)^2 = 6^2 + x^2 + 6^2 + (x-5)^2

Multiply out and simplify to

x^2 - 5x -36 = 0

Factor the quadratic: ((x-9)(x+4)=0  Therefore x=9 or x=-4.  We may disregard the negative answer so x = 9.  So PS is 9 and RP is 4.

Therefore entire hypotenuse is 4 + 9 or 13.