If the length of the sides of a triangle are in the ratio

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If the length of the sides of a triangle are in the ratio 4 : 5 : 6 and the inradius of the triangle is 3 cm, then the altitude of the triangle corresponding to the largest side as base is :

1. 7.5 cm
2. 6 cm
3. 10 cm
4. 8 cm

Correct Option: A

On the basis of given in question , we draw a figure a triangle ABC ,

The ratio of the sides of a triangle = 4 : 5 : 6
Let AB = 4y , BC = 5y , CA = 6y
∆OBA + ∆BOC + ∆AOC = ∆ABC

⇒	1	× 4y ×3 +	1	× 5y × 3 +	1	× 6y ×3 =	1	× 6y × h
	2		2		2		2

⇒ 6y +	15y	+ 9y = 3yh
	2

⇒ 12 + 15 + 18 = 6h
⇒ 45 = 6h

⇒ h =	15	= 7.5 cm
	2