Walking Under Ladders -- II

Geometry Level 4

An alley has both walls perpendicular to the ground.

Two ladders, one 3 feet long, the other 2 feet, are propped up from opposite bottom corners to the adjacent wall, forming an X shape.

All four legs of each ladder are firmly touching either the bottom corner or the opposite wall.

The two ladders are side by side and also touching each other at the intersection of the X shape.

The distance from the point of intersection to the ground (h)is 1 foot.

What is the width, \(w\) of the alley (in feet)? Given your answer to 2 decimal places.

The problem is not original.

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