The length of the hypotenuse of a right triangle is 10 cm, and the sum of the two right sides is 12 cm? Pythagorean theorem should be used

a^2+b^2 = c^2 = 100 ,a+b = 12
S=ab/2 =[(a+b)^2 - (a^2+b^2)]/4
=(144-100)/4
= 11

The sides of a right triangle are 6cm, 10cm and 8cm, respectively?

24.
6 8 10 is a Pythagorean triangle, 6 8 is a right angle side
(6*8)/2=24

If the hypotenuse of an isosceles right triangle is 10cm long, its area is

25 square centimeters
Make a vertical line to the hypotenuse
Get two small isosceles right triangles, right side length is 5
So the height of the original triangle is 5cm
So if the area equals the base times the height divided by 2, you get 25 square centimeters

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