In an isosceles triangle, the median of the lateral side is 10cm, the height lowered to the base is 16cm. Find the base of the triangle.

univerkov | March 2, 2021 | education

Since the ABC triangle is isosceles, the height of the BH lowered to the base of the AC is also the median of the ABM triangle.

The point of intersection of O, medians BH and AM divides them in a ratio of 2/1 starting from the apex of the triangles.

ВO / HO = 2/1.

ВO = 2 * OH.

ВН = 16 = ВO + OH = 3 * OH.

OH = 16/3 cm.

AO / MO = 2/1.

AO = 2 * MO.

AM = 10 = AO + MO = 3 * MO.

MO = 10/3 cm.

AO = 10 – 10/3 = 20/3 cm.

In a right-angled triangle AНO, AH ^ 2 = AO ^ 2 – OH ^ 2 = 400/9 – 256/9 = 144/9.

AH = 12/3 = 4 cm.

Then AC = 2 * AH = 2 * 4 = 8 cm.

Answer: The length of the base of the speaker is 8 cm.

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