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Дано (см. рисунок):

ΔABC - равнобедренный, AD = 250 см - высота, BC = 80.

ΔAB1C1 - равнобедренный, AD1 - высота, BC = 160.

BC II B1C1

Т.к. треугольники ABC и AB1C1 равнобедренные, то высоты AD и AD1 делят стороны BC и B1C1 пополам, т.е. BD = DC = 40 см, B1D1 = D1C1 = 80 см.

Рассмотрим ΔABD и ΔAB1D1:  

∠ABD=∠AB1D1, ∠A - общий, ∠ACD=∠AC1D1, как соответственные.

Следовательно, по первому признаку подобия, ΔABC подобен ΔAB1C1. Значит, по второму признаку подобия треугольников, AD/AD1 = BD/B1D1.

250/AD1 = 40/80 => AD1 = 250*80/40 = 500 см.