Question

a triangle having a perimeter 56 and it's sides are 2x,2x+3,and 2x+5. find the respective length of sides​

Answer 1

$\star \; {\underline{\boxed{\pmb{\blue{\sf{ \; Given \; :- }}}}}}$

• Perimeter of Triangle = 56 cm
• 1st side = 2x
• 2nd Side = 2x + 3
• 3rd side = 2x + 5

$\star \; {\underline{\boxed{\pmb{\pink{\sf{ \; To \; Find \; :- }}}}}}$

• Length of Sides = ?

$\star \; {\underline{\boxed{\pmb{\purple{\sf{ \; SolutioN \; :- }}}}}}$

$\dag$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Perimeter = A + B + C }}}}}$

Where :

• A = Side 1
• B = Side 2
• C = Side 3

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$\dag$ Calculating the Value of x :

${\dashrightarrow{\qquad{\sf{ Perimeter = A + B + C }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 56 = 2x + \bigg( 2x + 3 \bigg) + \bigg( 2x + 5 \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 56 = 2x + \bigg( 4x + 8 \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 56 = 6x + 8 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 56 - 8 = 6x }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 48 = 6x }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \dfrac{48}{6} = x }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \cancel\dfrac{48}{6} = x }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\color{darkblue}{\frak{ x = 8 }}}}}}}}$

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$\dag$ Calculating the Sides :

• ➳ Side 1 = 2x = 2(8) = 16 cm
• ➳ Side 2 = 2x + 3 = 2(8) + 3 = 19 cm
• ➳ Side 3 = 2x + 5 = 2(8) + 5 = 21 cm

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$\dag$ Therefore :

❛❛ The sides of the Triangle are 16 cm , 19 cm and 21 cm . ❜❜

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