∠ACB is an angle in the semicircle of diameter AB =

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∠ACB is an angle in the semicircle of diameter AB = 5 and AC : BC = 3 : 4. The area of the triangle ABC is

1. 6√2 sq. cm
2. 4 sq. cm
3. 12 sq. cm
4. 6 sq. cm

Correct Option: D

Angle at the semi-circle is a right angle.
∴ ∠ACB = 90°
AB = 5 cm.
AC = 3x cm. BC = 4x cm.
∴ (3x)² + (4x)² = (5)²
⇒ 9x² + 16x² = 25
⇒ 25x² = 25
⇒ x² = 1
⇒ x = 1

∴ Area of ∆ABC =	1	× BC × AC
	2

=	1	× 4 × 3 = 6 sq.cm.
	2