Find the area of the largest rectangle that can be inscribed in a right triangle

Question

Find the area of the largest rectangle that can be inscribed in a right triangle with legs of lengths 4 cm and 5 cm if two sides of the rectangle lie along the legs. I got 125/16 cm^2, but it is wrong. Maybe helpful: Keep in mind that the area of a rectangle with edges x and y is A = xy, and the edges are smaller than the legs of the triangle. Find a relationship between x and y, using properties of similar triangles. Rewrite the area as a function of one variable. Use calculus to find the edges of the rectangle that maximize the area

Explanation / Answer

A=xy (4-y)/y=x/(5-x) y=(4/5)(5-x) A=(4/5)(5-x)*x dA/dx=0 5-2x=0 x=5/2 y=2 A=xy=5

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