Question 80

The dimensions length, breadth and height of a wooden plank are in the ratio 4:5:7, and its surface area is 20086 square meters. Find the length of the plank.

Name: The dimensions length, breadth and height of a wooden plank are in the ratio 4:5:7, and its surface area is 20086 square meters. Find the length of the plank.
Uploaded: 2026-04-03T20:18:42.010410+05:30
Duration: 2 min 17 s
Description: The dimensions length, breadth and height of a wooden plank are in the ratio 4:5:7, and its surface area is 20086 square meters. Find the length of the plank.

Solution

Let the common factor be K

∴ Length = 4K ; Breadth = 5K and Height = 7K

Tip:

Total Surface area of cuboid = 2(LB + BH + LH)

L = Length; B = Breadth/width; H = Height

Whole surface area of the rectangular plank = 2(4K x 5K + 5K x 7K + 7K x 4K)

∴ 20086 = 83*2*K^2

∴ K = 11

∴ Length = 4K = 44 sq.m

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