The perimeter of the triangle MNK is 14.9 cm. MN is 1.5 times less than MK, and NK is 0.5 cm larger than MK.

| May 23, 2021 | education

The perimeter of the triangle MNK is 14.9 cm. MN is 1.5 times less than MK, and NK is 0.5 cm larger than MK. Find the length of each side.

Let the side MN of the triangle MNK be x cm, then the side MK is 1.5x cm (if MN is 1.5 times less than MK, then MK, on the contrary, is 1.5 times more than MN), and the side NK is (1.5x + 0 , 5) cm.By the problem statement, 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, P = MN + MK + NK) is (x + 1.5x + (1.5x + 0.5)) cm or 14.9 cm. Let’s make an equation and solve it.

x + 1.5x + (1.5x + 0.5) = 14.9;

x + 1.5x + 1.5x + 0.5 = 14.9;

4x + 0.5 = 14.9;

4x = 14.9 – 0.5;

4x = 14.4;

x = 14.4: 4;

x = 3.6 (cm) – MN;

1.5x = 3.6 * 1.5 = 5.4 (cm) – MK;

1.5x + 0.5 = 5.4 + 0.5 = 5.9 (cm) – NK.

Answer. MN = 3.6 cm; MK = 5.4 cm; NK = 5.9 cm.



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