Write down the expression for the perimeter of the triangle MNK and simplify it if: MN = a cm, NK is 30 cm

| August 2, 2021 | education

Write down the expression for the perimeter of the triangle MNK and simplify it if: MN = a cm, NK is 30 cm less than MN, and KM is 4 times more than NM. Make an equation and find the sides, knowing that the perimeter of triangle MNK is 108 cm.

Error in the condition: NK is 30 cm more than MN.
1. Let us express the NK side:
NK = MN + 30 = a + 30 (cm);
2. Let us express the KM side:
KM = MN * 4 = a * 4 = 4a (cm);
3. Let’s write the expression for the perimeter:
P = NK + MN + KM = a + a + 30 + 4a;
P = 6a + 30;
4. Substitute the perimeter value and find the sides:
6a + 30 = 108;
6a = 78;
a = 13;
That is, the side MN is 13 cm.
The KN side is 13 cm + 30 cm = 43 cm.
The KM side is 4 * 13 cm = 52 cm.
Answer: the lengths of the sides MN, KN and KM are respectively 13 cm, 43 cm, 52 cm.



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