Question

ACDE ~ APQR. CD = 9 m, EC = 15 m, PQ = 15 m. What is the length
of R.P?

Answer 1

To find the length of R.P, we need to first calculate the length of AC and then use this information to find the length of R.P.

Given that CD = 9 m, EC = 15 m, and PQ = 15 m, we can use the triangle similarity property in ACDE ~ APQR to find the length of AC:

AC / AP = CD / PQ
AC / AP = 9 / 15
AC / AP = 3 / 5
AC = (3/5) * AP

Now, we can use the fact that AC + EC = AP to find the length of AP:

AC + EC = AP
(3/5) * AP + 15 = AP
3AP + 75 = 5AP
75 = 2AP
AP = 37.5 m

Now that we have the length of AP, we can find the length of R.P using the triangle similarity property:

AC / AP = CD / PQ
AC / AP = 9 / 15
AC / 37.5 = 9 / 15
AC = (9/15) * 37.5
AC = 22.5 m

Since R.P is a part of PQ, R.P = PQ - AC = 15 - 22.5 = -7.5 m

Therefore, the length of R.P is 7.5 m.