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2 years ago

15.

Mathematics

1 answer:

frutty [35]2 years ago

5 0

Answer:

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.

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