D

R
P
For the triangle shown, RP = 24 and DP = 30.
what is the value of DR?
18
54
38.4
6

1 answer

To find the length of side \( DR \) in triangle \( RDP \), we can apply the Pythagorean theorem if triangle \( RDP \) is a right triangle.

We have:

  • \( RP = 24 \)
  • \( DP = 30 \)

Assuming \( DR \) is the unknown side \( x \), and applying the Pythagorean theorem:

\[ RP^2 + DR^2 = DP^2 \]

Substituting the known values:

\[ 24^2 + DR^2 = 30^2 \]

Calculating the squares:

\[ 576 + DR^2 = 900 \]

Now, isolate \( DR^2 \):

\[ DR^2 = 900 - 576 \]

\[ DR^2 = 324 \]

Now take the square root to find \( DR \):

\[ DR = \sqrt{324} = 18 \]

So, the value of \( DR \) is \( \boxed{18} \).