Question

each side of a triangle is increased by 10 cm if the ratio of the perimeter of the new triangle and the given triangle is 5 : 4 find the perimeter of givenTriangle​

Answer 1

Answer:

The perimeter of the given triangle is 120 cm.

Step-by-step-explanation:

Let the sides of the given triangle be a cm, b cm and c cm.

∴ Perimeter of given triangle = ( a + b + c ) cm

We have given that,

Each side of triangle is increased by 10 cm.

∴ The sides of the new triangle are

( a + 10 ) cm, ( b + 10 ) cm and ( c + 10 ) cm.

Now,

Perimeter of new triangle = ( a + 10 ) + ( b + 10 ) + ( c + 10 )

⇒ Perimeter of new triangle = a + 10 + b + 10 + c + 10

⇒ Perimeter of new triangle = a + b + c + 10 + 10 + 10

⇒ Perimeter of new triangle = ( a + b + c + 30 ) cm

Now, from the given condition,

P ( New triangle ) : P ( Given triangle ) = 5 : 4

$\displaystyle{\implies\sf\:(\:a\:+\:b\:+\:c\:+\:30\:)\::\:(\:a\:+\:b\:+\:c\:)\:=\:5\::4}$

$\displaystyle{\implies\sf\:\dfrac{(\:a\:+\:b\:+\:c\:+\:30\:)}{(\:a\:+\:b\:+\:c\:)}\:=\:\dfrac{5}{4}}$

$\displaystyle{\implies\sf\:4\:\times\:(\:a\:+\:b\:+\:c\:+\:30\:)\:=\:5\:\times\:(\:a\:+\:b\:+\:c\:)}$

$\displaystyle{\implies\sf\:4a\:+\:4b\:+\:4c\:+\:120\:=\:5a\:+\:5b\:+\:5c}$

$\displaystyle{\implies\sf\:120\:=\:5a\:+\:5b\:+\:5c\:-\:4a\:-\:4b\:-\:4c}$

$\displaystyle{\implies\sf\:5a\:-\:4a\:+\:5b\:-\:4a\:+\:5c\:-\:4c\:=\:120}$

$\displaystyle{\implies\sf\:a\:+\:b\:+\:c\:=\:120\:}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:Perimeter\:of\:given\ triangle\ =\ 120\ cm\ }}}}$