Topic: The circumference of a triangle is 24 cm, in which the sum of the two sides is equal to three times the length of the third side, and the difference between the two sides is equal to 1/2 of the length of the third side. Find the length of three sides of a triangle.

Solution: Let the three sides of the triangle be xcm.ycm.zcm

Then {x+y+z=24 ①.

{x+y=3z？ ②

{x-y= 1/2z③

Convert ① into: z = 24-x-y.

Substituting ② gives: x+y=3(24-x-y).

x+y=72-3x-3y

4x+4y=72

So x+y= 18, which means 3z= 18 z=6.

So ③x-y = 1/2×6 = 3? If the two equations are juxtaposed, there is {x+y= 18 x-y=3}

X= 10.5 y=7.5？

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