In an isosceles triangle, the base is 6, the lateral side is 5. From the apex of the triangle at the base and the apex

| May 10, 2021 | education

In an isosceles triangle, the base is 6, the lateral side is 5. From the apex of the triangle at the base and the apex opposite to the base, heights are drawn. The length of the smaller one is 4, find the length of the other height.

Since the height BH in an isosceles triangle is also the median of the triangle, then the segment AD = CD = AC / 2 = 6/2 = 3 cm. Then in the right-angled triangle ABH we determine the length of the height BH.

BH ^ 2 = AB ^ 2 = AD ^ 2 = 25 – 9 = 16.

BH = 4 cm.

Then the great height is AD.

Let us determine the area of the trapezoid through the base of the AC, the height BH.

Savs = AC * BH / 2 = 6 * 4/2 = 12 cm2.

Also, the area of the triangle ABC is equal to: Saws = BC * AD / 2 = 12 cm2.

Then AD = 24/5 = 4.8 cm.

Answer: The length of the height AD is 4.8 cm.



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