Question

The height of a wall is five times its width, and its length is eight times its height. If the volume of the wall is 12.8m^3, find its length.
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Answer 1

☊ GIVEN :-

⤋

➩ Volume of Wall = 12.8 m²

⤋

➩ Assume that the width of wall be x

⤋

➩ It is mentioned in question that height of a wall is five times its width so ⟶

⇶ height of wall ⟹ 5x

⤋

➩ It is mentioned in question that length is eight times its height so ⟶

⇶ length of wall ⟹ 8 × 5x

⇶length of wall ⟹ 40x

☊ To Find

➩ Length of wall = ?

☊ Explanation :-

⤋

⇶ Formula used :-

➩ Volume of wall = L × B × H

⇶ Where

➩ L means Length = 40 x

➩ B means Breadth = x

➩ H means Height = 5 x

☊ How to Solve :-

⤋

➩ Find the value of x using volume of wall formula that is length × breadth × height and then after finding value of x

➩ Place this value of x in length of wall = 40 x you will get your final answer

☊ Solution

⤋

➩ Volume of wall = L × B × H

⇶ Put given values in given Formula

⟴ Volume of wall

$\rm \implies \: 40x\: \times x \times 5x = 12.8$

$\rm \implies \: {200 \: x}^{3} = 12.8$

$\rm \implies \: { \: x}^{3} = \frac{12.8}{200}$

$\rm \implies \: { \: x}^{3} = \frac{12.8 \div 2}{200 \div 2}$

$\rm \implies \: { \: x}^{3} = \frac{6.4}{100}$

$\rm \implies \: { \: x}^{3} = \frac{64}{1000}$

$\rm \implies \: { \: x} = \frac{4}{10}$

$\bf\implies \: { \: x} = 0.4 \: m$

☊ Therefore

⤋

⇶length of wall ⟹ 40x

⇶ Place value of x in this

⌦ Therefore , length of wall

$\rm \implies \: 40 \times (0.4) = 16 \: m$

$\bf \implies \: 16 \: m$

⌦ Length of wall is

➲ 16 meters

Answer 2

To Find :

The length of the triangle

__________________________

Given :

• Length is 8 times its hieght
• Height is 5 times its width
• Volume = 12.8 m³

__________________________

Let's Assume:

• Breadth is x
• Hieght is 5x ('x' × 5)
• Length is 40x ('5x' × 8)

__________________________

Solution :

Given, Breadth = x

Hieght = 5x

Length = 40x

so, Volume = Breadth×length×hieght

$\implies \tt{12.8 = l \times b \times h}$

$\implies \tt{12.8 = 40x \times 5x \times x}$

$\implies \tt{12.8 = 200 {x}^{3} }$

$\implies \tt{x^{3} = \frac{12.8}{200}}$

$\tt{ \implies x = \sqrt[3]{ \frac{12.4}{200} } }$

$\implies \tt{x = \sqrt[3]{ \frac{1}{15.625} } }$

$\implies \tt{x = \sqrt[3]{ \frac{1}{15.625} } }$

$\implies \tt{x = \frac{1}{2.5} }$

$\implies \tt{x = 0.4}$

so, Breadth = 0.4 m

hieght = 0.4 × 5 m

or, hieght = 2 m

so, Length = 2×8 m

or, length = 16 m