Question

the lenghth of a rectangular plot is 5m more than its breath. if the perimeter of the plot is 74m, find the length and breadth.

Answer 1

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

$\text{The Length is 11 m}$

$\text{The Breadth is 6 m}$

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

$\textsf{\underline{\underline{Given :}}}$

Length of the Rectangle = 5 m more than Breadth.

Perimeter of Rectangle = 74 m

$\textsf{\underline{\underline{To find :}}}$

The Length and Breadth

$\textsf{\underline{\underline{Solution:}}}$

Consider the Breadth as x

Length = 5 + x

$\star$ Perimeter of Rectangle =

$\tt{\implies \:2(length + breadth)}$

$\tt{\implies2(5 + x + x) = 74}$

$\tt{\implies10 + 2x + 2x = 74}$

$\tt{\implies10 + 4x = 74}$

$\tt{\implies4x = 74 - 10}$

$\tt{\implies4x = 64}$

$\tt{\implies \: x = \dfrac{64}{4} }$

$\tt{\implies \: x = 16}$

${\boxed{\bigstar{\sf\:{x = 16}}}}$

Value of 5 + x =

$\tt{\implies \: x + 5}$

$\tt{\implies \:16 + 5}$

$\tt{\implies \:21}$

${\boxed{\bigstar{\sf\:{Length = 21 \:m}}}}$

${\boxed{\bigstar{\sf\:{Breadth = 16 \:m}}}}$

$\therefore$$\text{The Length is 11 m}$$\text{The Breadth is 6 m }$

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

$\tt{\implies2(5 + 16 + 16) = 74}$

$\tt{\implies10 + 32 + 32 = 74}$

$\tt{\implies10 + 64 = 74}$

$\tt{\implies74 = 74}$

Here, we subtituted the value of x with 16, which have us the required answer 74.

${\boxed{\sf\:{LHS = RHS}}}$

$\therefore$$\text{The Length is 11 m}$$\text{The Breadth is 6 m }$