Question

If the perimeter of a triangle is 6integer 2 by 3cm and the lengths of two of its sides are 2integer1by 2 cm and 3integer1 by 3find the length of three side.​

Answer 1

${\large{\bf{\red{\clubs{\underline{Given :}}}}}}$

${\sf{Perimeter = 6 \frac{2}{3} cm}}$

${\sf{1st \: Side = 2 \frac{1}{2}cm }}$

${\sf{2nd \: Side =3 \frac{1}{3} cm }}$

${\large{\bf{\blue{\clubs{\underline{To Find:}}}}}}$

${\sf{3rd \: side = ?}}$

${\large{\bf{\orange{\clubs{\underline{Solution :}}}}}}$

Formula for perimeter of triangle :

${\blue{\bigstar{\pink{\boxed{\mathfrak{Perimeter = a + b + c}}}}}}$

Here,

${\bf{\purple{A = 1st \: side}}}$

${\bf{\purple{B = 2nd \: side}}}$

${\bf{\purple{C = 3rd \: side}}}$

Now,

Let 3rd side be x:

Perimeter = A + B + C

${\mapsto{\bf{6 \frac{2}{3} = 2 \frac{1}{2} + 3 \frac{1}{3} + x}}}$

${\mapsto{\bf{ x = \frac{20}{3} - (\frac{5}{2} + \frac{10}{3}) }}}$

LCM of 2 and 3 = 6.

${\mapsto{\bf{ x = \frac{20}{3} - ( \frac{5 + 10}{6} ) }}}$

${\mapsto{\bf{ \frac{20}{3} - \frac{16}{6} }}}$

LCM of 3 and 6 = 6.

${\mapsto{\bf{ \frac{40 - 35}{6} }}}$

${\mapsto{\bf{ {\cancel\frac{5}{2} }}}}$

${\red = {\underline{\red{\bf{2 \frac{1}{2} cm }}}}}$

So,

${\mathfrak{\green{The \: 3rd \: side \: is \: 2 \frac{1}{2} cm.}}}$

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${\bf{\blue{\fcolorbox{green}{red}{\underline{XitzNobitaxX}}}}}$