Question

# The dimensions of a cuboid are in the ratio of 1 : 2 : 3 and its total surface area is 88 $$m^{2}$$.  Find the dimensions of the cuboid.

Solution

## Let length : breadth : height = 1 : 2 : 3$$\Rightarrow$$ l =x , b = 2x , h = 3xTSA of a cuboid = 2(lb+bh+lh)$$=2(x\times 2x+2x\times 3x+x\times 3x)$$$$= 2 (2x^{2}+6x^{2}+3x^{2})$$$$88m^{2} = 22x^{2}m^{2}$$$$\Rightarrow x^{2} = \frac{88}{22}\frac{m^{2}}{m^{2}}$$$$\therefore x = \pm 2$$So the dimensions are $$2\times 4\times 6$$Mathematics

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