Suppose ∆ ABC be a right-angled triangle where ∠A

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Suppose ∆ ABC be a right-angled triangle where ∠A = 90° and AD ⊥ BC. If ∆ ABC = 40 cm², ∆ ACD = 10 cm² and AC = 9 cm, then the length of BC is

According to question , we draw a figure right angled triangle CAB

In ∆ACD and ∆ABC,
∠CDA = ∠CAB = 90°
∠C is common.
∴ ∆ACD ~ ∆ABC

∴	∆ACD	=	AC²
	∆ABC		BC²

⇒	10	=	9²
	40		BC²

⇒ BC² = 4 × 9²
∴ BC = 2 × 9 = 18 cm