Question

10. Length of a rectangle is 3cm more than twice its breadth. Find the dimensions
of the rectangle if its perimeter is 78cm.
​

Answer 1

$\huge\fbox{Answer}$

$\large \underline{\underline{ \frak {\color{red}Given::}}}$

$\rightarrow \sf{Breadth \: of \: rectangle={ \rm{x}} \: cm}$

${ \rightarrow \sf{Length \: of \: rectangle={ \rm{2x+3}} cm}}$

$\rightarrow \sf{Perimeter \: of \: rectangle=78cm}$

$\large \underline{\underline{ \frak {\color{blue}To \: find::}}}$

$\sf \leadsto{Length \: and \: Breadth \: of \: the \: rectangle.}$

$\large \underline{\underline{ \frak {\color{gold}Formula \: required::}}}$

${ \small{ \star}} \fbox{\rm{Perimeter \: of \: rectangle=2(length + breadth)}} { \small{\star}}$

$\large \underline{\underline{ \frak {\color{peru}According \: to \: Question::}}}$

${\implies{\sf{Perimeter \: of \: rectangle=2(length + breadth)}}}$

${\implies{\sf{{78cm =2 (2x + 3 + x)}}}}$

${\implies{\sf{{ \frac{78}{2} cm = 2x + 3 + x}}}}$

${\implies{\sf{{ 39cm = 3x + 3 }}}}$

${\implies{\sf{{ 39cm - 3 = 3x }}}}$

${\implies{\sf{{ 36cm = 3x }}}}$

${\implies{\sf{{ x \: cm = \frac{36}{3} }}}}$

${\implies{\sf{{ x \: cm ={ \cancel{ \frac{36}{3}}} = 12cm}}}}$

$\large \underline{\underline{ \frak {\color{p}Hence,}}}$

${\implies \sf{Breadth \: of \: rectangle={ \rm{x}} \: cm} = 12cm}$

${ \implies \sf{Length \: of \: rectangle={ \rm{2x+3} } cm} = 2 \times 12cm + 3 = 27cm}$

$\large \underline{\underline{ \frak {\color{cyan}Verification::}}}$

${\mapsto{\sf{Perimeter \: of \: rectangle=2(length + breadth)}}}$

${\mapsto{\sf{78cm=2(27cm + 12cm)}}}$

${\mapsto{\sf{78cm=2 \times 39cm}}}$

${\mapsto{\sf{78cm=78cm}}}$

${\mapsto{\sf{L.H.S.=R.H.S.}}}$

$\large \underline{\underline{ \frak {\color{green}Formula \: related \: to \: rectangle::}}}$

${\mid {\boxed{ \begin{array}{ c | c } \hline \sf Perimeter_{(rectangle)}& \sf 2(length + breadth) \\ \hline \sf Area_{(rectangle)} & \sf length \times breadth \\ \hline \sf Diagonal_{(rectangle)}& \sf \sqrt{ {length}^{2} + {breadth}^{2} } \\ \end{array}}} \mid}$

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