One side of the triangle is 2.5 times smaller than the second and 16 cm smaller

| September 6, 2021 | education

One side of the triangle is 2.5 times smaller than the second and 16 cm smaller than the third. Find the sides of the triangle if its perimeter is 52 cm.

Let one side of the triangle be x cm, then the second side is equal to 2.5x cm, and the third side is equal to (x + 16) cm (if the first side is 2.5 less than the second and 16 less than the third, then the second side, on the contrary, is 2.5 times more, and the third is 16 more than the first). By the condition of the problem, it is known that the perimeter of a triangle (the perimeter of a triangle is equal to the sum of the lengths of its three sides) is equal to (x + 2.5x + (x + 16)) cm or 52 cm.Let’s make an equation and solve it.

x + 2.5x + (x + 16) = 52;

x + 2.5x + x + 16 = 52;

4.5x = 52 – 16;

4.5x = 36l

x = 36: 4.5;

x = 8 (cm) – 1st side;

2.5x = 8 * 2.5 = 20 (cm) – 2nd side;

x + 16 = 8 + 16 = 24 (cm) – 3rd side.

Answer. 8 cm, 20 cm, 24 cm.



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