The perimeter of the isosceles triangle ABC with the base of the AC is 28 cm.Find the height of the ВD

| February 10, 2021 | education

The perimeter of the isosceles triangle ABC with the base of the AC is 28 cm.Find the height of the ВD if the perimeter of the DBC triangle is 18 cm.

We are given an isosceles triangle ABC with a height ВD. Based on the properties of an isosceles triangle, the height drawn to the base is the median and the height.
If the ВD height is the median, then AD = AH.
The perimeter of any geometric figure is equal to the sum of the lengths of its sides.
We are given the perimeter of triangle ABC. Since triangle ABC is isosceles, its sides are equal, which means AB = BC.
The AВD and DCB triangles are equal to each other on those equal sides (AD = DС, AB = BC and ВD – common side).
Thus, we can find the sum of the sides AB = BC and AD = DС. To do this, divide the perimeter of the ABC triangle by 2:
AB + AD = BC + DС = 28: 2 = 14 cm.
We are given the perimeter of the DCB triangle, we need to find the height of the DВ. We know the sum of the sides of the BC and the DC, which means we can find the side of the DC. Let us denote the perimeter by the letter P.
R (DCB) = BC + DС + DВ.
DВ = R (DCB) – (ВС + DС) = 18-14 = 4 cm.
Answer: DВ = 4 cm.



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