Question

16. A rectangular plot of land is 50 m wide. The cost of fencing the plot at the rate of
18 per metre is 4680. Find
(i) the length of the plot.​

Answer 1

QUESTION :

• ➬ A rectangular plot of land is 50 m wide. The cost of fencing the plot at the rate of Rs. 18 per metre is Rs. 4680. Find the length of the plot.

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SOLUTION :

❖ Given :-

• Width of the rectangular plot = 50 m

• Cost of fencing the rectangular plot per meter = Rs. 18

• Cost of fencing the whole rectangular plot = Rs. 4680

❖ To Find :-

• Length of the rectangular plot = ?

❖ Required formula :-

$\bigstar \: \: \boxed{ \rm{ \: Perimeter \: \: of \: \: rectangle = 2 \: ( Length + Width ) \: }}$

❖ Calculation :-

• It is given that, cost of fencing the plot at the rate of Rs. 18 per metre is Rs. 4680.

Hence,

$\bigstar \: \: \sf{Perimeter \: \: of \: \: the \: \: plot = \dfrac{ \: Total \: \: cost \: \: of \: \: fencing \: \: the \: \: plot \: }{Cost \: \: of \: \: fencing \: \: per \: \: metre} } \\ \\ \: \: \: \: \: \:=\sf{ \large{ \dfrac{Rs. \: 4680}{Rs. \: 18} }} \\ \\ \: = \sf{ \large{ 260 \: m}}$

Suppose,

• Length of the rectangular plot = l

According to question,

$\: \: \: \: \: \bigstar \: \: \: \sf{ \large{ 2(l + w) = Perimeter}} \\ \\ \sf{ \large{ \implies \: 2 ( l + 50) = 260 }} \\ \\ \sf{ \large{ \implies \: l + 50 = \frac{260}{2} }} \: \: \: \: \\ \\ \sf{ \large{ \implies \: l + 50 = 130}} \: \: \: \: \\ \\ \sf{ \large{ \implies \: l = 130 - 50}} \: \: \: \\ \\ \sf{ \large{ \therefore \: \: \underline{ \: l = 80 \: }}}$

• Hence, length of the rectangular plot, l = 80 m

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ANSWER :

• ➫ If rectangular plot of land is 50 m wide. The cost of fencing the plot at the rate of Rs. 18 per metre is Rs. 4680, then the length of the plot is 80 m.