Question

a ladder is leaning against a wall. the foot of the ladder is 6 feet away from the wall, and the ladder reaches a point on the wall that is 10 feet above the ground. how long is the ladder? 12 feet 14 feet 8 feet

Explanation:

Step1: Apply Pythagorean theorem

The ladder, wall, and ground form a right triangle, where the ladder is the hypotenuse $c$. The theorem is $c = \sqrt{a^2 + b^2}$, with $a=6$ ft (distance from wall) and $b=10$ ft (height on wall).

Step2: Calculate squared side lengths

$6^2 = 36$, $10^2 = 100$

Step3: Sum squared lengths

$36 + 100 = 136$

Step4: Compute square root

$\sqrt{136} = \sqrt{4 \times 34} = 2\sqrt{34} \approx 11.66$ feet, which is closest to 12 feet.

Answer:

12 feet