The perimeter of a right triangle is 90 cm. Find the area of the triangle if the hypotenuse is 41 cm.

P = 90 cm;
P = a + b + c; perimeter of a right triangle;
c = 41 cm;
a + b + 41 = 90;
a + b = 49;
a = 49 – b;
a2 + b2 = c2; by the Pythagorean theorem;
(49 – b) 2 + b2 = 412;
2401 – 98 * b + b2 + b2 – 1681 = 0;
2 * b2 – 98 * b + 720 = 0;
b2 – 49 * b + 360 = 0;
D = 961;
Find the legs of the triangle:
b1 = 40 cm; a1 = 9 cm;
b2 = 9 cm; a2 = 40 cm;
Then the area of the triangle is:
S = ½ * a * b;
S = ½ * 40 * 9 = 180 cm2.