MO, MN, and ON are the midsegments of △JKL. What is the perimeter of △JKL? 6 9.5 11.5 19
2 answers:
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Answer:
4√13
Step-by-step explanation:
1. Calculate the length of SN
Your triangle (below) is a relatively tall isosceles triangle.
∆STN is a right triangle, so we can use Pythagoras theorem to calculate the length of SN.
SN² + NT² = ST²
SN² + 4² =22²
SN² + 16 = 484
SN² = 468
SN = √468 = 6√13
2. Calculate the length of SX
UM and SN are lines from an angle to the centre of the opposite side, so they are medians.
The medians of a triangle meet at a single point, X — the centroid.
Another characteristic is that the centroid divides each median into segments in a 2:1 ratio.
Thus,
SX = ⅔SN = ⅔ × 6√13 = 4√13
