Предмет: Геометрия, автор: vikaboichenko9

Основи прямокутної трапеції дорівнюють 5см 14см, а більша бічна сторона 15см. Знайдіть меншу діагональ трапеції.

Ответы

Автор ответа: Пеппер

Ответ:

13 см

Объяснение:

Дано: КМРТ - трапеція, МК⊥КТ; МР=5 см, КТ=14 см, РТ=15 см. КР - ?

Проведемо висоту РН. КН=МР=5 см, ТН=14-5=9 см

ΔРТН - прямокутний,

за теоремою Піфагора РН=√(15²-9²)=√(225-81)=√144=12 см.

ΔКРН - прямокутний, за теоремою Піфагора

КР=√(12²+5²)=√(144+25)=√169=13 см.

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