The base of an isosceles triangle is 4√2 and the median is drawn to the side 5 find the side of the triangle.

| August 2, 2021 | education

From vertex B, we lower the height BH in an isosceles triangle, which is also the bisector and median.

According to the property of the medians of the triangle, at the point of their intersection, they are divided into two segments in a ratio of 2/1, starting from the vertex.

Then AO / KO = 2/1.

Let KO = X cm, then AO = 2 * X.

KO + AO = 5 cm.

X + 2 * X = 5.

X = 5/3 cm.

KO = 5/3 cm.

AO = 5 – 5/3 = 10/3 cm.

From the right-angled triangle AOH, by the Pythagorean theorem, we define the leg OH.

OH ^ 2 = AO ^ 2 – AH ^ 2 = (10/3) ^ 2 – (2 * √2) ^ 2 = 100/9 – 8 = 28/9.

OH = √28 / 3 = (2 * √7) / 3 cm.

Then OB = 2 * OH = 4 * √7 / 3 cm.

BН = ОВ + ОН = (2 * √7) / 3 + (4 * √7) / 3 = 2 * √7 cm.

From the right-angled triangle ABH we define the hypotenuse AB.

AB ^ 2 = BH ^ 2 + AH ^ 2 = (2 * √7) ^ 2 + (2 * √2) ^ 2 = 28 + 8 = 36.

AB = 6 cm.

Answer: The side of the trapezoid is 6 cm.



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