SOLUTION: Quadrilateral PQRS has right angles at P and R. If PQ=9, PS=12, and QR=10, find RS. Thanks.

Algebra ->  Polygons -> SOLUTION: Quadrilateral PQRS has right angles at P and R. If PQ=9, PS=12, and QR=10, find RS. Thanks.      Log On


   

Question 1011929: Quadrilateral PQRS has right angles at P and R. If PQ=9, PS=12, and QR=10, find RS. Thanks.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
In quadrilateral PQRS ,
vertex P is adjacent to vertices Q and S .
Since there is a right angle at P ,
triangle PQS is a right triangle with hypotenuse QS ,
and legs PQ=9 and PS=12 .
Using the Pytahagorean theorem, we can find hypotenuse QS :
QS%5E2=PQ%5E2%2BPS%5E2
QS%5E2=9%5E2%2B12%5E2=81%2B144=225 and QS=sqrt%28225%29=15 .

In quadrilateral PQRS ,
vertex R is adjacent to vertices Q and S .
Since there is a right angle at R ,
triangle RQS is a right triangle with hypotenuse QS=15 ,
and legs QR=10 and PS .
Using the Pytahagorean theorem, we can find leg PS :
QS%5E2=QR%5E2%2BPS%5E2
225=10%5E2%2BPS%5E2--->225=100%2BPS%5E2--->225-100=PS%5E2 .
So, PS%5E2=125--->PS=sqrt%28125%29}--->highlight%28PS=5sqrt%285%29%29 .
If you want an approximate measure, highlight%28PS=about11.18%29 (rounded).