Đáp án:
Giải thích các bước giải:
Gọi $AB$ $=$ $3a$ ; $AC$ $=$ $4a$ .
Ta có:
$BC$² $=$ $AB$² $+$ $AC$²⇔ $125$² $=$ ( $3a$ )² $+$ ( $4a$ )²
⇔ $9a$² $+$ $16a$² $=$ $125$²
⇔ $25a$² $=$ $125$²
⇔ $a$² $=$ $125$² $÷$ $5$² $=$ $625$ .
⇔ $a$ $=$ $√625$ $=$ $25$
⇒ $AB$ $=$ $3$ $×$ $25$ $=$ $75$ ; $AC$ $=$ $4$ $×$ $25$ $=$ $100$
Ta có: $AB$² $=$ $BC$ $×$ $BH$ ⇔ $BH$ $=$ $AB$² $÷$ $BC$ $=$ $75$² $÷$ $125$ $=$ $45$
$AC$² $=$ $BC$ $×$ $CH$ ⇔ $CH$ $=$ $AC$² $÷$ $BC$ $=$ $100$² $÷$ $125$ $=$ $80$ .
