Question

The breadth of a cuboid is half it's length and it's height is 4cm. if the volume is 200cm², Find it's length and breadth.
Step by step!!​

Answer 1

Given :

• Breadth of a cuboid is half it's length
• Height of the cuboid = 4 cm
• Volume of the cuboid = 200 cm²

To Find :

• The length and breadth of the cuboid

Solution :

Let the length of the cuboid be x . Then it's breadth becomes "$\sf{\dfrac{x}{2}}$" {given condition}

Volume of a cuboid is given by ,

$\\ \star \: {\boxed{\purple{\sf{Volume_{(cuboid)} = length \times breadth \times height}}}}$

Substituting the values we have in the formula ,

$\\ : \implies \sf \: 200 = x \times \frac{x}{2} \times 4$

$\\ : \implies \sf \: 200 = x \times x \times 2$

$\\ : \implies \sf \: 200 = 2 {x}^{2}$

$\\ : \implies \sf \: {x}^{2} = \frac{200}{2 }$

$\\ : \implies \sf \: {x}^{2} = 100$

$\\ : \implies \sf \: x = \sqrt{100}$

$\\ : \implies{\underline{\boxed{\blue {\mathfrak{x = 10}}}}} \: \bigstar$

Then length and breadth of the cuboid are,

• Length = x = 10 cm

• Breadth = $\sf{\dfrac{10}{2}}$ = 5 cm

Hence ,

• The length and breadth of the givem cuboid are 10 cm and 5 cm

Answer 2

Answer:

Given :-

• The breadth of a cuboid is half of its length and its height is 4 cm and also it's volume is 200 cm².

To Find :-

• What is the length and breadth of the cuboid.

Formula Used :-

$\boxed{\bold{\small{Volume\: of\: Cuboid\: =\: Length\: \times Breadth\: \times Height}}}$

Solution :-

Let, the length of the cuboid be x.

And, the breadth will be half of its length, so the breadth will be $\sf\dfrac{x}{2}$.

Given :

• Length = x cm
• Breadth = $\sf\dfrac{x}{2}$ cm
• Height = 4 cm
• Volume = 200 cm²

According to the question by using the formula we get,

↦ $\sf x \times \dfrac{x}{2} \times 4 =\: 200$

↦ $\sf x \times \dfrac{x}{\cancel{2}} \times {\cancel{4}} =\: 200$

↦ $\sf x \times x \times 2 =\: 200$

↦ $\sf 2{x}^{2} =\: 200$

↦ $\sf {x}^{2} =\: \dfrac{\cancel{200}}{\cancel{2}}$

↦ $\sf {x}^{2} =\: 100$

↦ $\sf x =\: \sqrt{100}$

➦ $\sf\red{ x =\: 10\: cm}$

Hence, the required length and breadth are,

✧ Length = x = 10 cm

✧ Breadth = $\sf\dfrac{x}{2} =\: \dfrac{10}{2}$ = 5 cm

$\therefore$ The length of cuboid is 10 cm and the breadth of cuboid is t cm .