Question

what is the perimeter of a quadrilateral whose four sides measure 19 /6 centimetre 11 / 4 cm,53 / 12 Cm And 5 / 2 cm.​

Answer 1

$\bf \: \underline{Given }:$ ↴

$\sf \: Four \: sides \:of \:quadrilateral \: are \: \dfrac{19}{6}, \: \dfrac{11}{4}, \: \dfrac{53}{12}, \: \dfrac{5}{2}$

$\bf \: \underline{To \: find }:$ ↴

$\sf \: We \: have \: to \: find \: the \: Perimeter \: of \: the \: quadrilateral.$

$\bf \red{ \star }\: \underline{So, \:Let's \: Start }\: \red{\star}$

$\sf \: As \: we \: know \: that,$

$\boxed{ \pink{ \sf \: Perimeter \: of \: the \: quadrilateral = Sum \: of \: all \: sides}}$

$\sf \: Putting \: the \: values$

$\sf \: \longrightarrow \: \dfrac{19}{6} + \: \dfrac{11}{4} + \: \dfrac{53}{12} + \: \dfrac{5}{2}$

$\sf \: Finding \: the \: common \: denominator$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:6 - 4 - 12 - 2\:\:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:3 - 2 - 6 - 1\:\:\:}} \\\underline{\sf{3}}&{\underline{\sf{\:\:3 - 1 - 3 - 1\:\:\:}}} \\ \underline{\sf{}}&{\sf{\:\:1 - 1 - 1 - 1\:\:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\sf \: LCM = \underline{ 2 \times 2\times3} \: = \: 12$

$\longrightarrow \: \sf \dfrac{19}{6} \times \dfrac{2}{2} = \dfrac{38}{12}$

$\longrightarrow \: \sf \: \dfrac{11}{4} \times \dfrac{3}{3} = \dfrac{33}{12}$

$\longrightarrow \: \sf \dfrac{53}{12} \times \dfrac{1}{1} = \dfrac{53}{12}$

$\longrightarrow \: \sf \dfrac{5}{2} \times \dfrac{6}{6} = \dfrac{30}{12}$

$\sf \: Now, \: we \: have \: to \: add \: \: \dfrac{38}{12}, \: \dfrac{33}{12}, \: \: \dfrac{53}{12}, \: \dfrac{30}{12}$

$\sf \: \longrightarrow \: \: \dfrac{38}{12} + \: \dfrac{33}{12} + \: \: \dfrac{53}{12} + \: \dfrac{30}{12}$

$\sf \: Taking \: denominators \: as \: common$

$\sf \: \longrightarrow \: \: \dfrac{38 + 33 + 53 + 30}{12}$

$\sf \: Now, \: we \: will \: add \: the \: numerators$

$\sf \: \longrightarrow \: \: \dfrac{154}{12}$

$\sf \: Cancel \: the  \: common \: factor  \: of  \: 154 \:  and \:  12$

$\sf \: \longrightarrow \: \dfrac{154 \div 2}{12 \div 2} \: = \dfrac{77}{6}$

$\green{ \sf \: So, \: Perimeter \: of \: quadrilateral = \dfrac{77}{6} \: cm}$

$\sf \: Answer :$ ↴

$\sf \bull \longrightarrow \: In \: Fraction = \dfrac{77}{6}$

$\sf \bull \longrightarrow \: In \: Decimal = 12.83 \: cm$

$\sf \bull \longrightarrow \: In \:Mixed \: Fraction = 12 \dfrac{5}{6}$