Question

1. if a ladder reaches 12 feet up a wall and the base is 5 feet from the wall, how long is the ladder?

a. 14 feet
b. 13 feet
c. 10 feet
d. 12.5 feet

Explanation:

Step1: Identify right - triangle

The wall, the ground and the ladder form a right - triangle, where the height on the wall is one leg ($a = 12$ feet) and the distance from the base of the ladder to the wall is the other leg ($b = 5$ feet), and the ladder is the hypotenuse ($c$).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. Substitute $a = 12$ and $b = 5$ into the formula: $12^{2}+5^{2}=c^{2}$, so $144 + 25=c^{2}$, and $c^{2}=169$.

Step3: Solve for $c$

Take the square root of both sides. Since $c>0$, $c=\sqrt{169}=13$ feet.

Answer:

B. 13 feet