Question

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

Answer 1

Step-by-step explanation:

GIVEN:-

=>Dimensions of a cuboid are in the ratio 5:3:1.

=>Total surface area of cuboid is 414m^2.

=>Length=5x

=>Breadth=3x

=>Height=x

TO FIND:-

=>The values of dimensions.

$\tt\fbox\purple{Understanding The Concept}$

According to the question,

=>We know that the ratios of the dimensions are 5:3:1 and the total surface area is 414m^2.

=>From this we can find the values of dimensions from the formula of total surface area of cuboid,

$\bf{ = > 2(lb + bh + hl)}$

$\huge\bf\underline{Answer}$

Using the given formula,

$\bf{ 414 =2(5x \times 3x + 3x \times x + 5x \times x) }$

$\bf{414 = 2(15x {}^{2} + 3x {}^{2} + 5x {}^{2} )}$

$\bf{414 = 2 \times 23x {}^{2} }$

$\bf{207 = 23x {}^{2} }$

$\bf{x {}^{2} = \dfrac{207}{23} }$

$\bf{}x {}^{2} = 9$

$\bf{}x = 3$

Therefore, the values of dimensions,

Length= 5x=>15m

Breadth=3x=>9m

Height=x=>3