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A Triangle in a Square (Posted on 2019-08-21) Difficulty: 3 of 5
ABCD is a square with points E and F on sides AB and BC respectively. Given DF=4, EF=3, and DE=5 find the area of the square.

No Solution Yet Submitted by Brian Smith    
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Solution Geometer's Sketchpad approximation | Comment 1 of 6
Using Geometer's Sketchpad to construct a rectangle about a rotatable triangle of the given dimensions, the height and width of the rectangle are equal when both are 3.88057, making the area 15.05882.

I defined the lengths in inches, to make the figures look a reasonable size, but the measurements came out in centimeters, but I converted back to inches and square inches, though GSP claimed they were still cm and cm^2 as I divided by pure numbers.

Wolfram Alpha suggests the value I got could be 256/17, but that may be no more meaningful than just a continued fraction approximation that could be done on any decimal number.

Edited on August 21, 2019, 10:26 am
  Posted by Charlie on 2019-08-21 10:18:54

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