bigtriangleup ABC is right-angled triangle where m ∠ ABC = 90ᵒ. If m (AB̅) = 15 cm, m (BC̅) = 20 cm, and BD̅ bot AC̅ , intersecting AC̅ at the point D, find m (BD̅) (in cm).

bigtriangleup ABC is right-angled triangle where m ∠ ABC =…

$\bigtriangleup$ ABC is right-angled triangle where m $\angle$ ABC = 90^o. If m $(\overline{AB})$ = 15 cm, m $(\overline{BC})$ = 20 cm, and $\overline{BD}$ $\bot$ $\overline{AC}$ , intersecting $\overline{AC}$ at the point D, find m $(\overline{BD})$ (in cm).

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 12.

Pythagoras theorem, AC² = AB² + BC²

BD = (AB × BC)/AC

According to the given question,

In the above figure, usin Pythagoras theorem,

AC² = AB² + BC²

⇒ AC² = 15² + 20²

⇒ AC² = 225 + 400

⇒ AC² = 625

⇒ AC = 25 cm

Now, BD = (AB × BC)/AC

⇒ BD = (15 × 20)/25

⇒ BD = 12 cm

SSC CHSL 2024 PYQ — Question 75