For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
10/06/2016

Problem 1
A rhombus, ABCD, has sides of length 10. A circle with center A passes through C (the opposite vertex.) Likewise, a circle with center B passes through D. If the two circles are tangent to each other, what is the area of the rhombus?

Problem 2
Two ladders are placed cross-wise in an alley to form a lopsided X-shape. The walls of the alley are not quite vertical, but are parallel to each other. The ground is flat and horizontal. The bottom of each ladder is placed against the opposite wall. The top of the longer ladder touches the alley wall 5 feet vertically higher than the top of the shorter ladder touches the opposite wall, which in turn is 4 feet vertically higher than the intersection of the two ladders. How high vertically above the ground is that intersection?

An alley, with two sloping, but parallel, walls. The ladders are placed cross-wise.

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Problems from 09/22/16

Problem 1
What is the area of triangle whose sides are 2, 3, and 4 meters in length?

Problem 2
What is the maximum possible area of quadrilateral whose sides are 2, 3.4, and 5 meters in length?

Congratulations to Ramachandran Balakrishna, who was the winner of the last set of puzzles.

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