Question

Correctly label the sides of the triangle shown below(3 points)
Drop target 1
Drop target 2
Drop target 3
Question 2
For the triangle shown above, RP¯¯¯¯¯¯¯¯ =24, and DR¯¯¯¯¯¯¯¯=7
, which of the following the correct way to set up the problem to find DP?(2 points)
Responses

x2+72=242
x squared plus 7 squared is equal to 24 squared

24+7=x
24 plus 7 is equal to x

x2+242=72
x squared plus 24 squared is equal to 7 squared

242+72=x2
24 squared plus 7 squared is equal to x squared
Question 3
What is DP? Round your answer to the nearest tenth if necessary(2 points)
DP =

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Answer 1

To label the sides of the triangle, we'll assume the triangle has vertices D, P, and R. Here's how the labeling works based on the sides provided:

- Let DP be the side opposite to the base (RP).
- Let RP = 24 (given).
- Let DR = 7 (given).

### Question 2:

To find the value of DP based on the information provided and the triangle's properties, we can apply the Pythagorean theorem.

Given:
- RP = 24 (hypotenuse or side opposite to the right angle)
- DR = 7 (one of the other sides)

We set up the equation as follows to find DP:

\[
DP^2 + DR^2 = RP^2
\]
\[
x^2 + 7^2 = 24^2
\]

### So the correct way to set up the problem is:

**x^2 + 7^2 = 24^2** (This matches the option "x squared plus 7 squared is equal to 24 squared.")

### Question 3:

Now to find DP (which we will denote as x):

From the equation, we can express it fully:

\[
x^2 + 49 = 576
\]

Subtract 49 from both sides:

\[
x^2 = 576 - 49
\]
\[
x^2 = 527
\]

Now take the square root of both sides to solve for x:

\[
x = \sqrt{527} \approx 22.9 \, (after rounding to the nearest tenth)
\]

### So,

**DP ≈ 22.9**