It is known that the sum of the right sides of a right triangle is equal to 8. What is the maximum area of the right triangle when the two right sides are equal to each other?

Let a and B be the lengths of two right angle sides respectively, then a + B = 8, then B = 8-a. according to the area formula: S = 1 / 2 * a * b = 1 / 2 * a * (8-A) = - 1 / 2 (A-2) (A-2) + 2, when a and B are 2 and 6 respectively, the triangle has the largest area, and the largest area is 2

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