Find the legs of a right-angled triangle if their sum is 46 cm, and the hypotenuse of the triangle is 34 s.

Let X cm – the length of one leg, and Y cm – the length of the other leg.
Let us write down the conditions of the first problem in the form:
X + Y = 46
X = 46 – Y
By the Pythagorean theorem
X ^ + Y ^ = 34 ^
Substitute the expression for the unknown X into the second equation:
(46 – Y ^) + Y ^ = 34 ^
2116 – 92 * Y + 2 * Y ^ = 1156
2 * Y ^ – 92 * Y + 960 = 0
Divide both sides of the equation by 2
Y ^ – 46 * Y + 480 = 0
D = 2116 – 1920 = 196, root (D) = 14
Y (1) = (46 + 14) / 2 = 30, X (1) = 46 – 30 = 16
Y (2) = (46 – 14) / 2 = 16, X (2) = 46 – 16 = 30
Pairs (X1, Y1) and (X2, Y2) are symmetric, so we will write one of them in our answer.
Answer: 16 cm; 30 cm.