Предмет: Математика, автор: arturpr

В прямоугольном треугольнике один катет меньше гипотенузы на 18 см, а другой - на 9 см. Найдите гипотенузу.

Ответы

Автор ответа: lara164

пусть х - гипотенуза, тогда (х-18) - первый катет, (х-9) - второй катет
по теореме пифагора
(х-18)²+(х-9)² = х²
х²-36х+324+х²-18х+81=х²
х²-54х+405=0
D =27²-405*1=324 √D =18
x₁=27-18=9 - не подходит по смыслу задачи, слишком маленькое значение
х₂ = 27+18=45 (см) - длина гипотенузы
Ответ: 45 см

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