In triangle STR, medians TT1, SS1 and RR1 intersect at point O. Line segments OR1 = OS1 = OT1 = root of 8 dm.

| January 8, 2021 | education

In triangle STR, medians TT1, SS1 and RR1 intersect at point O. Line segments OR1 = OS1 = OT1 = root of 8 dm. Find the area of a triangle STR

By the property of the medians of the triangle, they are divided in the ratio of 2/1 at the point of their intersection.
Since, by condition, OR1 = OS1 = OT1, then OR = OS = OT, and therefore, then the medians of the triangle are equal.
If the medians of a triangle are equal, then such a triangle is equilateral.
Let’s determine the length of the median TT1.
TT1 = OT1 + 2 * TT1 = √8 + 2 * √8 = 3 * √8 cm.
The median of an equilateral triangle is also its height, then TT1 = SP * √3 / 2.
SP = 2 * TT1 / √3 = 2 * 3 * √8 / √3 = 2 * √3 * √8 = 2 * √24 = 4 * √6 cm.
Then Sstr = SR * TT1 / 2 = 4 * √6 * 3 * √8 / 2 = 6 * √48 = 24 * √3 cm2.
Answer: The area of the triangle is 24 * √3 cm2.



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