Find the height CH of an isosceles triangle ABC (AC = BC) if the perimeter of triangle ABC is 26

Find the height CH of an isosceles triangle ABC (AC = BC) if the perimeter of triangle ABC is 26 and the perimeter of triangle ACN is 18.

Since the triangle ABC is isosceles with the base AB, then the height of CH is at the same time the median dividing the base AB in half, which means AH = BH. The perimeter of the triangle ABC: PABC = AC + BC + AB, but since AC = BC, and AB = AH + BH, you can write:

PABC = AC + AC + AH + AH = 2 * (AC + AH).

Hence, AC + AH = PABC / 2 = 26/2 = 13 cm.

Perimeter of triangle ACH: PACH = AC + AH + CH.

Let’s find the height of CH: CH = PACH – AC – AH = PACH – (AC + AH) = 18 – 13 = 5 cm.