The height drawn from the top of an isosceles triangle cuts off a triangle from it, the perimeter

| September 9, 2021 | education

The height drawn from the top of an isosceles triangle cuts off a triangle from it, the perimeter of which is 18 cm.Calculate the length of the height if the perimeter of this isosceles triangle is: a) 24 cm. B) 30 cm. C) 20 cm.?

The perimeter of triangle ABD will be equal to:

Ravd = AB + BD + AD = AB + BD + AC / 2 = 18 cm.

Since the triangle is isosceles, the perimeter of the BCD triangle is also 18 cm.

If two heights BD are subtracted from the sum of the perimeters of triangles ABD and BCD, then we get the perimeter of triangle ABC.

Ravd + Rvsd – 2 * BD = Ravs.

2 * BD = 2 * Ravd – Ravs.

BD = (2 * Ravd – Rav) / 2. (1).

ВD = (2 * 18 – 24) / 2 = 6 cm.

Substitute the remaining values into equation 1.

ВD = (2 * 18 – 30) / 2 = 6/2 = 3 cm.

ВD = (2 * 18 – 20) / 2 = 16/2 = 8 cm.

Answer: Height BD is equal to: a) 6 cm, b) 3 cm, c) 8 cm.



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