Question

a 300 m long wire is used to fence a rectangular plot whose length is twice its width find the length and breadth of the plot

Answer 1

$\textbf{\large{\underline{Answer :-}}}$

The Length is 100 m and Breadth is 50 m

$\textbf{\large{\underline{Explanation :-}}}$

$\textsf{\large{Given :-}}$

Length of the wire used to Fence the Rectangle = 300 m

$\textsf{\large{To find :-}}$

Length and Breadth of Rectangle

$\textsf{\large{Solution :-}}$

As given in the question, length is twice its Breadth (width) So,

$\tt{\rightarrow Breadth = x }$

$\tt{\rightarrow Length = 2x }$

The Length of the wire to Fence is actually the Perimeter of the Rectangle.

$\textbf{Perimeter of Rectangle=}$

$\tt{\rightarrow 2(Length+Breadth) }$

$\tt{\Rightarrow 2(2x+x)=300}$

$\tt{\Rightarrow 4x + 2x= 300}$

$\tt{\Rightarrow 6x=300}$

$\tt{\Rightarrow x = \dfrac{300}{6} }$

$\tt{\Rightarrow x = \dfrac{50}{1} }$

$\tt{\Rightarrow x = 50 \: m}$

Length =

$\tt{\Rightarrow 2x}$

$\tt{\Rightarrow 2 \times 50}$

$\tt{\Rightarrow 100 \: m}$

$\textbf{Length = 100m}$

Breadth =

$\tt{\Rightarrow x}$

$\tt{\Rightarrow x = 50 \: m}$

$\textbf{Breadth = 50 m }$

$\therefore$The Length is 100 m and Breadth is 50 m

$\textbf{\large{\underline{Verification :- }}}$

$\tt{\Rightarrow2(100 + 50) = 300}$

$\tt{\Rightarrow200 + 100 = 300}$

$\tt{\Rightarrow300 = 300}$

$\therefore$LHS = RHS

$\therefore$The Length is 100 m and Breadth is 50 m