Correctly label the sides of the right triangle shown below(3 points)

Question

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

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

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

Answer 1

To correctly label the sides of the right triangle, we need to identify the sides based on the information given:

1. \( RP \) is the hypotenuse (the longest side of the right triangle).
2. \( DR \) is one of the legs of the triangle.
3. \( DP \) is the remaining leg we need to find.

With that setup, let's approach the questions:

Question 2: Correct Way to Set Up the Problem to Find DP

Given:

• \( RP = 24 \) (Hypotenuse)
• \( DR = 7 \) (One leg)
• \( DP \) (The other leg, we want to find)

Using the Pythagorean Theorem, which states that \( a^2 + b^2 = c^2 \) (where \( c \) is the hypotenuse):

The equation to set up would be:

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

So we have:

\[ DP^2 + 7^2 = 24^2 \]

This means the correct option is:

x² + 7² = 24²

Question 3: What is DP?

To find \( DP \):

1. Substitute the values into the equation from Question 2: \[ DP^2 + 7^2 = 24^2 \] \[ DP^2 + 49 = 576 \]

2. Solve for \( DP^2 \): \[ DP^2 = 576 - 49 \] \[ DP^2 = 527 \]

3. Take the square root of both sides to find \( DP \): \[ DP = \sqrt{527} \approx 22.9 \]

Therefore, rounding to the nearest tenth, the length of \( DP \) is:

DP ≈ 22.9