Question
Download Solution PDFThe height of a right triangular prism is 21 cm and the ratio of the sides of its base is 8 : 15 : 17. If the total area of the three lateral surfaces is 840 cm2, then what is the volume of the prism in cubic centimetre?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven,
Height of the triangular prism is h = 21 cm
The ratio of sides of triangular prism is = 8x : 15x : 17x
The total area of three lateral surfaces is = 840 cm2
Perimeter of the triangle × height = 840
⇒ (8x + 15x + 17x) × 21 = 840
⇒ 40x = 840/21
⇒ x = 40/40
⇒ x = 1
Sides of the triangular prism are 8, 15 and 17.
As we know,
⇒ s = (a + b + c)/2
⇒ s = (8 + 15 + 17)/2
⇒ s = 40/2 = 20
Area of the triangle = √[s (s – a) (s – b) (s – c)]
Area of the triangle = √[20 × (20 – 8) (20 – 15) (20 – 17)]
Area of the triangle = √[20 × 12 × 5 × 3]
Area of the triangle = 60
As we know,
Volume of the prime = Area of Base × height
Volume of triangular prism = 60 × 21 = 1260 cm3
Last updated on Jul 17, 2025
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