Question

The ratio between length and breadth of a field is 10 : 6. The area of the field is 3840m². Find the difference between the length and width of the field
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Answer 1

Corrected Question :

• The ratio between length and breadth of a rectangular field is 10 : 6. The area of the rectangular field is 3840m². Find the difference between the length and width of the rectangular field.

A N S W E R :

• The difference between the length and width of the rectangular field 32 m.

Given :

• The ratio between length and breadth of a field is 10 : 6. The area of the rectangular field is 3840².

To find :

• Find the difference between the length and width of the rectangular field ?

$\large\star$ As we know that,

$\large\dag$ Formula Used :

• $\boxed{\bf{Area\: of\: rectangle\:=\: Length\:×\: Breadth}}$

Solution :

• Area = 3840 cm²

• Length = 10x

• Breadth = 6x

• Value of Length and Breadth = ${\sf{10x\:×\:6x\:=}}$60x²

$~~~~~$

:$\implies$${\sf{60x^2\:=\:3840}}$

$~~~~~$

$~~~~~$:$\implies$${\sf{x^2\:=\; \dfrac{3840}{60}}}$

$~~~~~$

$~~~~~~~~~~$:$\implies$${\sf{x^2\:=\; \cancel{\dfrac{3840}{60}}}}$

$~~~~~$

$~~~~~~~~~~~~~~~$:$\implies$${\sf{x^2\:=\:64^2}}$

$~~~~~$

$~~~~~~~~~~~~~~~~~~~~$:$\implies$${\underline{\boxed{\frak{\pink{x\:=\:8}}}}}$★

$~~~~~$

• Length = 10 × 8 = 80 m

• Breadth = 6 × 8 = 48 m

• Difference = 80 - 48 = 32 m

Hence,

• ${\underline{\sf{The \:difference \:between \:the \:length \:and \:width\: of \:the\: \bf{rectangular}\: \sf{field}\; \bf{32\:m}.}}}$

$~~~~$$\qquad\quad\therefore{\underline{\textsf{\textbf{Hence, Verified!}}}}$

$~~~~~~~~~~~~~~~$ _____________________

Answer 2

Step-by-step explanation:

$\huge{\bf{\green{\mathfrak{\dag{\underline{\underline{Question:-}}}}}}}$

$\bullet{\longmapsto}$ The ratio between length and breadth of a field is 10 : 6. The area of the field is 3840m². Find the difference between the length and width of the field.

$\huge {\bf{\orange{\mathfrak{\dag{\underline{\underline{Answer:-}}}}}}}$

$\bullet{\leadsto} \: \textsf{The ratio between length and breadth of a field is 10:6.}$

$\bullet{\leadsto} \: \sf Area \: of \: the \: field \: = \: 3840m^{2}.$

$\bullet{\leadsto} \: \textsf{Let the length and breadth of the field be x.}$

$\bullet{\leadsto} \: \pink{\tt Then, \: Length \: = \: 10x.}$

$\bullet{\leadsto} \: \pink{\tt Then, \: Breadth \: = \: 6x.}$

$\bullet{\leadsto} \: \pink{\tt Area \: = \: 3840m^{2}.}$

$\bullet{\leadsto} \: \therefore{\sf l \: * \: b \: = \: 3840m^{2}.}$

$\bullet{\leadsto} \: \textsf{Substituting the values,}$

$\bullet{\leadsto} \: \sf 10x \: * \: 6x \: = \: 3840$

$\bullet{\leadsto} \: \sf 60x^{2} \: = \: 3840$

$\bullet{\leadsto} \: \sf x^{2} \: = \: \dfrac{384\cancel{0}}{6\cancel{0}}$

$\bullet{\leadsto} \: \sf x^{2} \: = \: \dfrac{\cancel{384}}{\cancel{6}}$

$\bullet{\leadsto} \: \sf x^{2} \: = \: 64$

$\bullet{\leadsto} \: \sf x \: = \: \sqrt{64}$

$\bullet{\leadsto} \: \underline{\boxed{\purple{\tt x \: = \: 8.}}}$

$\bullet{\leadsto} \: \textsf{Now finding length and breadth,}$

$\bullet{\leadsto} \: \sf Length \: = \: 10x \: = \: 10 \: * \: 8 \: = \: 80m.$

$\bullet{\leadsto} \: \sf Breadth \: = \: 6x \: = \: 6 \: * \: 8 \: = \: 48m.$

$\bullet{\leadsto} \: \pink{\texttt{Difference between length and breadth =}}$

$\bullet{\leadsto} \: \sf l \: - \: b$

$\bullet{\leadsto} \: \sf 80 \: - \: 48$

$\bullet{\leadsto} \: \underline{\boxed{\purple{\tt Difference \: = \: 32 \: m.}}}$

$\huge{\bf{\red{\mathfrak{\dag{\underline{\underline{Conclusion:-}}}}}}}$

$\bullet{\longmapsto} \: \boxed{\therefore{\sf Difference \: between \: length \: and \: breadth \: of \: the \: field \: = \: 32 \: m.}}$

$\huge{\bf{\blue{\mathfrak{\dag{\underline{\underline{Formulas \: Used:-}}}}}}}$

$\bullet{\leadsto} \: \underline{\sf Area \: of \: Rectangle \: = \: l \: * \: b.}$

$\bullet{\leadsto} \: \sf where,$

$\bullet{\leadsto} \: \sf l \: is \: Length$

$\bullet{\leadsto} \: \sf b \: is \: Breadth$

:)