Question

If the ladder is 10 m long and 5 m from the base of the building, how high up the building will the ladder reach?

(1 point)
Responses

52+x2=102; x = √75 m, which is an irrational number and would be estimated to be 8.7 m.
5 squared plus x squared is equal to 10 squared ; x = √75 m, which is an irrational number and would be estimated to be 8.7 m.

102−−−√+52=c2; c = √125, which is an irrational number and must be estimated at 11.2 m.
square root of 10 squared end root plus 5 squared is equal to c squared ; c = √125, which is an irrational number and must be estimated at 11.2 m.

52+x2=102; x = 75 m, which is a rational, whole number
5 squared plus x squared is equal to 10 squared ; x = 75 m, which is a rational, whole number

102+52=c2; c = 125 m, which is a rational, whole number

Answer 1

To find out how high the ladder will reach on the building, we can use the Pythagorean theorem. The ladder forms a right triangle with the ground and the side of the building, where:

- The length of the ladder is the hypotenuse (\(c = 10 \, \text{m}\)).
- The distance from the base of the building is one leg of the triangle (\(b = 5 \, \text{m}\)).
- The height up the building is the other leg of the triangle (\(a\), which we are trying to find).

According to the Pythagorean theorem:

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

Substituting in the values we have:

\[ a^2 + 5^2 = 10^2 \]

This becomes:

\[ a^2 + 25 = 100 \]

Now, subtract 25 from both sides:

\[ a^2 = 100 - 25 \]
\[ a^2 = 75 \]

Now, take the square root of both sides:

\[ a = \sqrt{75} \]
\[ a = 5\sqrt{3} \]

Since \( \sqrt{75} \) is approximately 8.7 m, the ladder will reach approximately 8.7 m up the building.

So the correct response would be:

"5 squared plus x squared is equal to 10 squared; x = √75 m, which is an irrational number and would be estimated to be 8.7 m."