The length, breadth and height of a rectangular solid are in the ratio 5 : 4 : 2. If the total surface area is 1216 cm², find the length, the breadth and the height of the solid.
Mensuration
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Question

The length, breadth and height of a rectangular solid are in the ratio 5 : 4 : 2. If the total surface area is 1216 cm2, find the length, the breadth and the height of the solid.

KnowledgeBoat · Accepted Answer

Given: Total surface area = 1216 cm2 Ratio of dimensions = 5 : 4 : 2 Let the sides of rectangular solid be 5a, 4a and 2a. Total surface area = 2(lb \+ bh \+ hl) ⇒ 2(5a x 4a \+ 4a x 2a \+ 2a x 5a) = 1216 cm2 ⇒ 2(20a2 \+ 8a2 \+ 10a2) = 1216 cm2 ⇒ 2 x 38a2 = 1216 cm2 ⇒ 76a2 = 1216 cm2 ⇒ a2 = cm2 ⇒ a2 = 16 cm2 ⇒ a = cm ⇒ a = 4 cm Dimensions of rectangular solid are: Length = 5a = 5 x 4 cm = 20 cm Breadth = 4a = 4 x 4 cm = 16 cm Height = 2a = 2 x 4 cm = 8 cm Hence, length, breadth and height of rectangular solid are 20 cm, 16 cm and 8 cm, respectively.

Mathematics

The length, breadth and height of a rectangular solid are in the ratio 5 : 4 : 2. If the total surface area is 1216 cm², find the length, the breadth and the height of the solid.

Mensuration

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