A 15 m ladder rests against a window 9 m above the ground on one side of a street. Keeping the foot fixed, it is turned to the other side to reach a window 12 m high. Find the width of the street.

Introduction / Context:This is a classic two right-triangles setup sharing the same ladder length and foot position. Horizontal reaches to each wall add to the street width.

Given Data / Assumptions:

• Ladder length L = 15 m.
• Heights: 9 m on one side, 12 m on the other.

Concept / Approach:For each side, horizontal distance to the wall is the base of a right triangle with hypotenuse 15 and vertical leg equal to the window height. Sum the two bases to get the street width.

Step-by-Step Solution:

Verification / Alternative check:Both bases are positive and consistent with the Pythagorean theorem; the same hypotenuse is used in each orientation.

Why Other Options Are Wrong:30 m or 31 m double-count or miscompute the square roots; 12 m is just one side’s base.

Common Pitfalls:Using 9 + 12 under the square root; forgetting to add bases from both walls.

Final Answer:21 m