Let ABCDEF be a prism whose base is a right angled triangle,

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Let ABCDEF be a prism whose base is a right angled triangle, where sides adjacent to 90° are 9 cm and 12 cm. If the cost of painting the prism is Rs. 151.20, at the rate of 20 paise per sq cm then the height of the prism is :

1. 17 cm
2. 18 cm
3. 15 cm
4. 16 cm

Correct Option: B

Total surface area of prism =	151.2.	=	1215	= 756 sq.cm.
	0.20		2

Hypotenuse of the triangular base = √9² + 12² = √81 + 144
= √225 = 15 cm.
∴ Perimeter of base = 9 + 12 + 15 = 36 cm.
∴ Total surface area = Perimeter of base × height + 2 × area of base

⇒ 756 = 36 × h + 2 ×	1	× 9 × 12
	2

→756 = 36h + 108
⇒ 36h = 756 – 108 = 648

⇒ h =	648	= 18 cm.
	36