The perimeter of an equilateral triangle MNP is 21 cm, point K is marked on the side MN

| February 4, 2021 | education

The perimeter of an equilateral triangle MNP is 21 cm, point K is marked on the side MN, so the length of segment MK is 2 cm, find the length of segment KP.

It is known that the perimeter of an equilateral triangle MNP is 21 cm, which means that in order to find the side of an equilateral triangle MNP, you need to divide the perimeter of the triangle by 3, because the triangle is equilateral:

21: 3 = 7 (cm) – side length of an equilateral triangle;

Point K is marked on the side MN so that the length of the segment MK is 2 cm, we draw the segment KP.

Consider triangle MKP:
MK = 2 cm, MP = 7 cm, ∠KMP = 60 ° (by the property of an equilateral triangle).
By the cosine theorem, we find the length KP:
KP² = MK² + MP² – 2 * MK * MP * cos ∠KMP;
KP² = 4 + 49 – 28 * 0.5;
KP² = 39;
KP = √39 (cm)
Answer: √39 cm.



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