# The Dimensions of a Cuboid Are in the Ratio 5 : 3 : 1 and Its Total Surface Area is 414 M2. Find the Dimensions. - Mathematics

The dimensions of a cuboid are in the ratio 5 : 3 : 1 and its total surface area is 414 m2. Find the dimensions.

#### Solution

$\text { It is given that the sides of the cuboid are in the ratio 5: 3: 1 } .$

$\text { Suppose that its sides are x multiple of each other, then we have: }$

$\text { Length = 5x m }$

$\text { Breadth = 3x m }$

$\text { Height = x m }$

$\text { Also, total surface area of the cuboid = 414 }m^2$

$\text { Surface area of the cuboid = 2 }\times (\text { length } \times \text { breadth + breadth } \times \text { height + length }\times \text { height })$

$\Rightarrow 414 = 2 \times (5x \times 3x + 3x \times 1x + 5x \times x)$

$\Rightarrow 414 = 2 \times (15 x^2 + 3 x^2 + 5 x^2 )$

$\Rightarrow 414 = 2 \times (23 x^2 )$

$\Rightarrow 2 \times (23 \times x^2 ) = 414$

$\Rightarrow (23 \times x^2 ) = \frac{414}{2} = 207$

$\Rightarrow x^2 =\frac{207}{23} = 9$

$\Rightarrow x = \sqrt{9} = 3$

$\text { Therefore, we have the following: }$

$\text { Lenght of the cuboid = 5 } \times x = 5 \times 3 = 15 m$

$\text { Breadth of the cuboid = 3 } \times x = 3 \times 3 = 9 m$

$\text { Height of the cuboid = x = 1 } \times 3 = 3 m$

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 21 Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)
Exercise 21.3 | Q 6 | Page 22