Предмет: Геометрия, автор: nastyshka9onelove

Знайти діагоналі паралелограма, якщо їхні довжини відносяться як 4:7, а сторони порівнюють 7см і 9 см

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Автор ответа: Пеппер

Нехай діно АВСД - паралелограм, АС і ВД діагоналі, АС\ВД=4\7. ВС=9 см, АВ=7 см. Знайти АС і ВД.

За властивістю діагоналей паралелограма АС²+ВД²=2(АВ²+ВС²)=2(49+81)=2*130=260.

Нехай АС=4х, тоді ВД=7х одиниць.

(4х)²+(7х)²=260

16х²+49х²=260

65х²=260

х²=4

х=2.

АС=7*2=14 (од.), ВД=4*2=8 (од.)

Відповідь: 14; 8.

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