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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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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☊ 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
[tex] \rm \implies \: 40x\: \times x \times 5x = 12.8[/tex]
[tex]\rm \implies \: {200 \: x}^{3} = 12.8[/tex]
[tex]\rm \implies \: { \: x}^{3} = \frac{12.8}{200} [/tex]
[tex]\rm \implies \: { \: x}^{3} = \frac{12.8 \div 2}{200 \div 2} [/tex]
[tex]\rm \implies \: { \: x}^{3} = \frac{6.4}{100} [/tex]
[tex]\rm \implies \: { \: x}^{3} = \frac{64}{1000} [/tex]
[tex]\rm \implies \: { \: x} = \frac{4}{10} [/tex]
[tex]\bf\implies \: { \: x} = 0.4 \: m[/tex]
☊ Therefore
⤋
⇶length of wall ⟹ 40x
⇶ Place value of x in this
⌦ Therefore , length of wall
[tex] \rm \implies \: 40 \times (0.4) = 16 \: m[/tex]
[tex] \bf \implies \: 16 \: m[/tex]
⌦ Length of wall is
➲ 16 meters
Verified answer
To Find :
The length of the triangle
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Given :
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Let's Assume:
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Solution :
Given, Breadth = x
Hieght = 5x
Length = 40x
so, Volume = Breadth×length×hieght
[tex] \implies \tt{12.8 = l \times b \times h}[/tex]
[tex] \implies \tt{12.8 = 40x \times 5x \times x}[/tex]
[tex] \implies \tt{12.8 = 200 {x}^{3} }[/tex]
[tex] \implies \tt{x^{3} = \frac{12.8}{200}} [/tex]
[tex] \tt{ \implies x = \sqrt[3]{ \frac{12.4}{200} } }[/tex]
[tex] \implies \tt{x = \sqrt[3]{ \frac{1}{15.625} } }[/tex]
[tex] \implies \tt{x = \sqrt[3]{ \frac{1}{15.625} } }[/tex]
[tex] \implies \tt{x = \frac{1}{2.5} }[/tex]
[tex] \implies \tt{x = 0.4}[/tex]
so, Breadth = 0.4 m
hieght = 0.4 × 5 m
or, hieght = 2 m
so, Length = 2×8 m
or, length = 16 m