To solve this problem, we can use the Pythagorean theorem. In this scenario, the ladder forms a right triangle with the building and the ground.
The lengths of the sides of the triangle are:
- The length of the ladder (hypotenuse): \( c = 24 \) feet
- The distance from the base of the ladder to the building (one leg of the triangle): \( a = 6 \) feet
- The height of the ladder on the building (the other leg of the triangle): \( b \)
According to the Pythagorean theorem, we have:
\[ a^2 + b^2 = c^2 \]
Substituting the known values into this equation:
\[ 6^2 + b^2 = 24^2 \]
Calculating \( 6^2 \) and \( 24^2 \):
\[ 36 + b^2 = 576 \]
Now, subtract 36 from both sides:
\[ b^2 = 576 - 36 \]
\[ b^2 = 540 \]
To find \( b \), we take the square root of both sides:
\[ b = \sqrt{540} \]
Calculating the square root of 540 gives us:
\[ b \approx 23.24 \text{ feet} \]
So, the height up the building where the top of the ladder touches is approximately 23.24 feet. Based on the options you've given, the correct response would be:
6 squared plus b squared is equal to 24 squared ; 23.24 ft.