Впрямоугольном треугольнике abc с прямым углом c проведена средняя линия mn параллельная катету ac найдите длину ac если am= корень из 3 bn=корень из 2

средняя линия треугольника делит стороны ab и cb на равные отрезки am и mb, cn и nb соответственно. следовательно, ab = am + mb = √3 + √3 = 2√3, cb = cn + nb = 2√2.

по теореме пифагора найдем сторону ас: ac² + cb² = ab²

ac² = (2√3)² - (2√2)² = 12 - 8 = 4

ac = 2

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