Question

A ladder 15 m long reaches a window 12 m above the ground. Find the distance of the foot of the ladder from the building.

• A. 5 m
• B. 9 m
• C. 12 m
• D. 15 m

Hint:

Always check for Pythagorean triplets like (3,4,5). Here (9,12,15) is a scaled version of it, which makes solving instant without full calculation.

Answer 1

The Correct Option is B

Concept: This is a right-angled triangle problem formed by a ladder leaning against a wall. The ladder acts as the hypotenuse, the wall height is one perpendicular side, and the ground distance is the base. We use the Pythagorean theorem: \[ a^2 + b^2 = c^2 \] where:
• \(c\) = ladder length (hypotenuse)
• \(a\) = height of wall
• \(b\) = distance from wall

Step 1: Identify given values. \[ c = 15 \text{ m}, \quad a = 12 \text{ m}, \quad b = ? \]

Step 2: Apply Pythagorean theorem. \[ 12^2 + b^2 = 15^2 \]

Step 3: Compute squares carefully. \[ 144 + b^2 = 225 \]

Step 4: Isolate \(b^2\). \[ b^2 = 225 - 144 \] \[ b^2 = 81 \]

Step 5: Take square root. \[ b = \sqrt{81} = 9 \]

Step 6: Final interpretation. The distance from the foot of the ladder to the building is: \[ 9 \text{ m} \] Final Answer: \[ \boxed{9 \text{ m}} \]