Question

I don’t understand need it by tomorrow!

Answer 1

Explanation:

It can help to draw your own figure with the right angles better represented. You will notice that right triangles PQR and PRS share side RS. PQ is the hypotenuse of one of them; RS is the hypotenuse of the other.

We can write two equations that make use of the Pythagorean theorem:

  PQ² = PR² +RQ²

  RS² = QS² +RQ²

Then we can swap sides of the first equation and subtract the second equation. This gives ...

  (PR² +RQ²) -(RS²) = (PQ²) -(QS² +RQ²)

Adding RQ², we can write this as ...

  PR² -RS² +2RQ² = PQ² -QS²

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The given relationship PR > RS means that PR² -RS² will be positive, so the left side of this equation must be positive.

Since PQ² - QS² is a positive number, PQ > QS.

Answer 2

Step-by-step explanation:

In the right triangle PQR we have the side PQ is the hypotenuse then

PQ > PR

and since  PR > RS (given) then PQ > RS (1)

In the right triangle QRS we have the side RS is the hypotenuse then

RS > QS (2)

finally ,

(1) + (2) give us PQ > QS