A window needs to be replaced that is 7 feet high. If a ladder is placed 24 feet from the base of the window, how long must the ladder be to reach the window?

To find the length of the ladder needed to reach the window, we can use the Pythagorean theorem. The ladder, the distance from the base of the window to the base of the ladder, and the height of the window form a right triangle.

1. Let:
- \( a \) = the height of the window = 7 feet
- \( b \) = the distance from the base of the window to the base of the ladder = 24 feet
- \( c \) = the length of the ladder (the hypotenuse)

According to the Pythagorean theorem:

\[
c^2 = a^2 + b^2
\]

2. Substitute the known values into the formula:

\[
c^2 = 7^2 + 24^2
\]
\[
c^2 = 49 + 576
\]
\[
c^2 = 625
\]

3. Now, take the square root to find \( c \):

\[
c = \sqrt{625} = 25
\]

Therefore, the length of the ladder must be **25 feet** to reach the window.

A window needs to be replaced that is 7 feet high. If a ladder is placed 24 feet from the base of the window, how long must the ladder be to reach the window?

To determine the length of the ladder needed to reach the window, we can apply the Pythagorean theorem. This theorem is applicable since the ladder, the height of the window, and the distance from the wall to the base of the ladder form a right triangle.

Here are the steps to solve the problem:

1. **Identify the variables:**
- Height of the window (\( a \)) = 7 feet
- Distance from the base of the window to the base of the ladder (\( b \)) = 24 feet
- Length of the ladder (\( c \)) = ?

2. **Use the Pythagorean theorem:**

\[
c^2 = a^2 + b^2
\]

3. **Plug in the known values:**

\[
c^2 = 7^2 + 24^2
\]
\[
c^2 = 49 + 576
\]
\[
c^2 = 625
\]

4. **Calculate \( c \):**

\[
c = \sqrt{625} = 25
\]

Thus, the length of the ladder must be **25 feet** to reach the window.

A wheelchair camp is constructed to rise 3 feet off the ground and extends 4 feet along the ground. How long will the wheelchair ramp be?

To find the length of the wheelchair ramp, we can use the Pythagorean theorem. The ramp forms the hypotenuse of a right triangle, where one leg is the height the ramp rises (3 feet), and the other leg is the distance it extends along the ground (4 feet).

Here are the steps:

1. **Identify the variables:**
- Height of the ramp (\( a \)) = 3 feet
- Distance along the ground (\( b \)) = 4 feet
- Length of the ramp (\( c \)) = ?

2. **Use the Pythagorean theorem:**

\[
c^2 = a^2 + b^2
\]

3. **Plug in the known values:**

\[
c^2 = 3^2 + 4^2
\]
\[
c^2 = 9 + 16
\]
\[
c^2 = 25
\]

4. **Calculate \( c \):**

\[
c = \sqrt{25} = 5
\]

Thus, the length of the wheelchair ramp will be **5 feet**.