Given that the sum of the three sides of a right triangle is a + B + C = 2 and C is the hypotenuse, the maximum area of a right triangle can be obtained

Given that the sum of the three sides of a right triangle is a + B + C = 2 and C is the hypotenuse, the maximum area of a right triangle can be obtained

When a = B, the area is the largest
When a = B, 2A + C = 2
2a²=c²
c=√2a
∴(√2＋2)a=2
a=2/(√2＋2)
=2-√2
In this case, the area s = AB / 2 = (6-2 √ 2) / 2
=3-√2

For a right triangle, the length ratio of the three sides is 3:4:5. The longest side is known to be 15 cm. What is the area of the triangle in square cm?

The lengths of the two right angles are as follows:
15÷5×3=9
15÷5×4=12
The area of triangle is: 12 × 9 △ 2 = 54

The difference between two right sides of a right triangle is 7cm, and the area is 30cm 2

Let the shorter right angle side length be xcm, the longer one be (x + 7) cm, 12x · (x + 7) = 30, and the result is as follows: x2 + 7x-60 = 0, ∧ (x + 12) (X-5) = 0, ∧ x = 5 or x = - 12 (rounding off). 5 + 7 = 12cm, 52 + 122 = 13cm. The length of hypotenuse is 13cm