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Find the length of the square that is possibly largest to fit into the triangle Our free triangle calculator computes the sides' lengths, angles, area, heights, perimeter, medians, and other parameters, as well as its diagram. The solution here is purely with the use of trigonometric ratios

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Given, the lengths of the sides of a right triangle (except hypotenuse) are 16 cm and 8 cm The pythagorean theorem states that if the square of one side of a triangle is greater than the sum of the squares of the other two sides, then the triangle is a right triangle. We have to find the length of the side of the largest square that can be inscribed in the triangle.

I have seen that the length of each side of the biggest square that can be inscribed in a right triangle is half the harmonic mean of the legs of the triangle

I have not seen a rigorous explanation for it, though. Find the length of the hypotenuse of the triangle using the pythagorean theorem Divide the hypotenuse by sqrt (2) to get the side length of the largest square that can fit inside the triangle Calculate the area of the square using the formula area = side_length * side_length.

Thus, the length of the side of the largest square that can be inscribed in triangle abc is approximately 5.33 cm For example, if you consider a triangle with a base and height of different lengths, you can visually see how the largest square fits within the triangle. If inscribed requires (as it usually does) that each vertex of the target square lie on an edge, then options would seem to be pretty limited But maybe the question is abusing the term to mean the largest square that fits in the space.

I am wondering how you would go about to find the largest square that would fit inside a triangle

An example of what i am asking is