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.​

Answer 1

Given: The ratio between length and breadth of a field is 10 : 6. The area of the field is 3840m²

To Find: Find the difference between the length and width of the field.

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❒ Let the length and breadth of the field be 10x and 6x respectively

${ \underline{ \bf{ \bigstar{According \: to \: the \: question : }}}}$

• The Area of the rectangle is 3840cm² and we'have to find the difference between the length and breadth

Now,

• Let's firstly find the length and breadth of the rectangle and then find their difference

As we know that,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dag \: \bigg[ \bf \: Area _{(recatngle)} = l \times b \bigg]$

Here,

• Length = 10x
• Breath = 6x
• Area = 3840cm²

Substituting we get,

${ : \implies} \rm \: Area _{(rectangle)} = lenght \times breadth \\ \\ \\ { : \implies} \rm \: 3840 {cm}^{2} = 10x \times 6x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \: 3840 {cm}^{2} = 60 {x}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm {x}^{2} = \frac{3840}{60}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm {x}^{2} = 64\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm x = \sqrt{64} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm{ \boxed{ \frak{x = 8cm}}}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Now let's find the length and breadth

$\longrightarrow \tt \: lenght = 10x = 80cm \\ \\ \\ \longrightarrow \tt breadth= 6x = 48cm \: \:$

• Now let's find the difference

$\longrightarrow \tt 80cm - 48cm \\ \\ \longrightarrow \tt{ \pink { \boxed{ \frak{32cm}} \star}} \: \: \: \: \: \: \: \: \:$

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$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Given :

• The ratio between length and breadth of a field is 10 : 6.
• Area of Field = 3840m²

To Find :

• the difference between the length and breadth of the field.

Solution :

➞ Let the Length be 10p

➞ Let the Breadth be 6p

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✰ As we know that, Area of Rectangle is given by Length × Breadth so simply we will put the given values in the formula to find the measure of length and breadth after that we will substract them to find the difference between length and breadth.

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⠀⠀⟼⠀⠀Area of Rectangle = L × B

⠀⠀⟼⠀⠀3840 = 10p × 6p

⠀⠀⟼⠀⠀3840 = 60p²

⠀⠀⟼⠀⠀3840/60 = p²

⠀⠀⟼⠀⠀64 = p²

⠀⠀⟼⠀⠀√64 = p

⠀⠀⟼⠀⠀8m = p

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Therefore :

⟿ Length of Rectangle = 10p

⟿ Length of Rectangle = 10 × 8

⟿ Length of Rectangle = 80m

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⟿ Breadth of Rectangle = 6p

⟿ Breadth of Rectangle = 6 × 8

⟿ Breadth of Rectangle = 48m

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Finding the Difference :

➣ Difference = Length - Breadth

➣ Difference = 80 - 48

➣ Difference = 32m

Thus Difference between the Length and Breadth is 32m

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