SOLUTION: PQRS is a rectangle in which PQ =10 CM AND PS =6CM .T IS A POINT ON PQ SUCH THAT RST IS AN ISOSCELES TRIANGLE WHOSE EQUAL SIDES ARE RS AND ST FIND RT

Algebra ->  Pythagorean-theorem -> SOLUTION: PQRS is a rectangle in which PQ =10 CM AND PS =6CM .T IS A POINT ON PQ SUCH THAT RST IS AN ISOSCELES TRIANGLE WHOSE EQUAL SIDES ARE RS AND ST FIND RT      Log On


   



Question 461150: PQRS is a rectangle in which PQ =10 CM AND PS =6CM .T IS A POINT ON PQ SUCH THAT RST IS AN ISOSCELES TRIANGLE WHOSE EQUAL SIDES ARE RS AND ST FIND RT
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let W be the point on SR such that |SW| = |PT|. Let x = |SW|. By the given, |SR| = |ST| = 10. Then %28ST%29%5E2+=+%28SW%29%5E2+%2B+6%5E2, or 10%5E2+=+x%5E2+%2B+6%5E2, or
100+=+x%5E2+%2B+36, or x = 8 after a little algebra.
Then %28RT%29%5E2+=+6%5E2+%2B+%2810+-+x%29%5E2, or %28RT%29%5E2+=+6%5E2+%2B+2%5E2+=+40, or
abs%28RT%29+=+sqrt%2840%29+=+2sqrt%2810%29 cm.