cde - pqr cd=9, ec=15, pq 15 .what is the length of rp

Answer 1

To find the length of RP, we need to use the triangle inequality theorem on triangle CDE.

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

Given: CD = 9, EC = 15, and PQ = 15

We know that CD + EC > DE and DE + PQ > CD

Substituting the given values:
9 + 15 > DE
24 > DE

Also,
15 + DE > 9
DE > -6

Since the length of a side cannot be negative, we only consider the positive value of DE:

DE > -6 becomes DE > 6

So, the length of DE must be greater than 6.

We also know that RP is the sum of EC, CD, and DE.

Therefore, RP = EC + CD + DE > 15 + 9 + 6 = 30

Therefore, the length of RP must be greater than 30.