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Find all sides of a right triangle whose perimeter is equal to 60 cm and its area is equal to 150 square cm.

Sagot :

Sabbieyidn

x + y + H = 60 : perimeter , x, y and H be the two legs and the hypotenuse of the right triangle

(1/2)xy = 150 : area

x2 + y2 = H2: Pythagora's theorem.

3 equations with 3 unknowns.

(x + y)2 - 2xy = H2 : completing the square in the third equation.

x + y = 60 - H : express x + y using the first equation and use the second equation to find xy = 300 and substitute in equation 5.

(60 - H)2 - 600 = H2 : one equation with one unknown.

Solve for H to find H = 25 cm. Substitute and solve for x and y to find x = 15 cm and y = 20 cm.