Question

Armaan has a rectangular garden of length and breadth. 168/5 m and 135/6 m respectively . Find the cost of fencing the garden 5 rounds at the rate of Rs 21/2 per metre.​

Answer 1

➤ Given :-

Length of the garden :- ${\tt \dfrac{168}{5}}$ m

Breadth of the garden :- ${\tt \dfrac{135}{6}}$ m

Cost of fencing per metre :- ${\tt \dfrac{21}{2}}$

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➤ To Find :-

Cost of fencing the garden 5 rounds.

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★ How to do :-

Here, we are given with the length and breadth of a rectangle garden. We are said that it should be fenced 5 rounds around that full park. We are asked to find the total rupees it costs to fence the whole park 5 times. So, first we should find the perimeter of that park by using the formula given below. Then, we should find the cost that it takes to fence the garden one time. Then, we can find the total cost by multiplying it by 5. So, let's solve!!

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➤ Solution :-

Perimeter of the park :-

${\tt \leadsto \underline{\boxed{\tt 2 \: (Length + Breadth)}}}$

Substitute the given values.

${\tt \leadsto 2 \: \bigg( \dfrac{168}{5} + \dfrac{135}{6} \bigg)}$

LCM of 5 and 6 is 30.

${\tt \leadsto 2 \: \bigg( \dfrac{168 \times 6}{5 \times 6} + \dfrac{135 \times 5}{6 \times 5} \bigg)}$

Multiply the numerators and denominators of both fractions in the bracket.

${\tt \leadsto 2 \: \bigg( \dfrac{1008}{30} + \dfrac{675}{30} \bigg)}$

Now, add the values in the bracket.

${\tt \leadsto 2 \: \bigg( \dfrac{1008 + 675}{30} \bigg)}$

Add the numerators in the bracket.

${\tt \leadsto 2 \: \bigg( \dfrac{1683}{30} \bigg)}$

Multiply the numbers.

${\tt \leadsto 2 \times \dfrac{1683}{30}}$

Multiply the numerator with numerator and the denominator with denominator.

${\tt \leadsto \dfrac{2 \times 1683}{30} = \dfrac{3366}{30}}$

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Now, let's find the cost of fencing the garden one time.

Cost of fencing the garden once :-

${\tt \leadsto \dfrac{3366}{30} \times \dfrac{21}{2}}$

Multiply the numerators and denominators at once.

${\tt \leadsto \dfrac{3366 \times 21}{30 \times 2} = \dfrac{70686}{60}}$

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Now let's fInd the cost of fencing it five times.

Cost of fencing the park five times :-

${\tt \leadsto \dfrac{70686}{60} \times 5}$

Write the denominator and the whole number in lowest form by cancellation method.

${\tt \leadsto \dfrac{70686}{\cancel{60}} \times \cancel{5} = \dfrac{70686}{12}}$

Now, simplify the fraction to get the final answer.

${\tt \leadsto \cancel \dfrac{70686}{12} = \pink{\underline{\boxed{\tt Rs \: \: 5890.5}}}}$

$\Huge\therefore$ The total cost of fencing the park five times is ₹5890.5.

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$\dashrightarrow$ Some related formulas :-

$\begin{gathered} \small \boxed{\begin{array} {cc} \large \dag \: \sf More \: Formulas \\ \\ \sf{\bigstar \: {Area}_{(Rectangle)} = Length \times Breadth} \\ \\ \sf{\bigstar \: {Length}_{(Rectangle)} = \dfrac{Perimetre}{2} - Breadth} \\ \\ \sf{\bigstar \: {Breadth}_{(Rectangle)} = \dfrac{Perimetre}{2} - Length} \\ \\ \sf{\bigstar \: {Length}_{(Rectangle)} = \dfrac{Area}{Breadth}} \\ \\ \sf{\bigstar \: {Breadth}_{(Rectangle)} = \dfrac{Area}{Length}} \end{array}} \end{gathered}$