Question

Look at triangle PQR.



Which statement about the sides of the triangle PQR is true?

The length of PQ is equal to the difference of the lengths of PR and RQ.

The length of PR is less than the sum of the lengths of PQ and RQ.

The length of PQ is greater than the sum of the lengths of PR and RQ.

The length of PR is equal to the difference of the lengths of PQ and RQ.

Answer 1

Ah for this question you need to remember just one thing:

A\(^2\) + B\(^2\) = C\(^2\)

;-)

Answer 2

how is the triangle doesnt have any numbers?

Answer 3

Your hypotenuse, C, is PQ here. It HAS TO be the longest

Answer 4

okay m choice would be c?

Answer 5

I would do it this way to check yourself, let RQ = 3, PR = 4, and PQ = 5 (keeps in order which is smaller or larger, the numbers themselves don't particularly matter here)

Go ahead and write out each of the statements with those numbers.

Answer 6

like that the dont i have to do 3^2+4^2=5^2?

Answer 7

\[3^2+4^2=5^2\]
is
9+16=25
25=25
So it's cool. :-)

Or if you prefer some more exact numbers that are close to what you have in the drawing:
RQ = 2\(\sqrt{2}\) (about 2.828), PR = \(\sqrt{17}\) (about 4.123), and PQ = 5
(check the squares of these, you'll see they work out with the Pythagorean Theorem ok)




Now true or false time:



PR is less than the sum of the lengths of PQ and RQ.
4 < 5 + 3
4 < 8
Obvious eh? :-) It's true/correct.

4.123 < 5 + 2.828
7.123 < 7.828
closer but still ok



The length of PQ is greater than the sum of the lengths of PR and RQ.
5 > 4 + 3
5 > 7
Nope/False.

5 > 4.123 + 2.828
5 > 6.951
False.



The length of PR is equal to the difference of the lengths of PQ and RQ
4 = 5 - 3
4 = 2
False.

4.123 = 5 - 2.828
4.123 = 2.172
False.

Answer 8

Now that's what I call a fully detailed response ^_^

Have a great day! :-)

Answer 9

This is one of those types of problems they are looking for you to do some creative problem solving in @rajfk35 . There's not some magic formula that can give you the answer (well outside of remembering the Pythagorean Theorem). :-D

Answer 10

The length of PR is less than the sum of the lengths of PQ and RQ. You can always us a compass to pick up the lenghts and place them next to each other and "see" the answer. If this is not intuitively obvious, then you can always assign arbritrary numbers to the sides of the triangle and use Pythagoras's theorem