The sides of the triangle are 10 cm and 15 cm, and the median to the third side is 8.5 cm.

| July 6, 2021 | education

The sides of the triangle are 10 cm and 15 cm, and the median to the third side is 8.5 cm. Find the third side of the triangle.

The length of the median of a triangle is found by the formula: m = 1 / 2√ (2 (a ^ 2 + b ^ 2) – c ^ 2), where m is the median, a and b are the sides of the triangle, c is the side of the triangle to which median. Substitute all known values into the formula and find the length of the third side c: 8.5 = 1 / 2√ (2 (10 ^ 2 + 15 ^ 2) – c ^ 2); 8.5 = 1 / 2√ (2 (100 + 225) – c ^ 2); 8.5 = 1 / 2√ (2 * 325 – c ^ 2); 8.5 = 1 / 2√ (650 – c ^ 2); 10√ (650 – c ^ 2) = 170 (according to the main property of the “cross to cross” proportion); √ (650 – c ^ 2) = 170/10; √ (650 – c ^ 2) = 17; 650 – c ^ 2 = 17 ^ 2; 650 – c ^ 2 = 289; – c ^ 2 = 289 – 650; – c ^ 2 = – 361; c ^ 2 = 361; c = √361; c = 19 cm.
Answer: c = 19 cm.



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