Question

Each side of a triangle is increased by 10 cm. If the ratio of the perimeters of the new triangle and the given triangle is 5:4, find the perimeter of the given triangle.

Answer 1

Given :

• Each side of a triangle is increased by 10 cm.
• The ratio of the perimeters of the new triangle and the given triangle is 5:4.

To find :

• The perimeter of the given triangle.

Solution :

Consider,

• Each side of triangle = x cm

Formula used :-

Perimeter of triangle = a+b+c

Then,

Perimeter of given triangle ,

= x+x+x = 3x cm

If each side of triangle is increased by 10, then side of new triangle will be (x+10) cm

Then ,

Perimeter of new triangle,

= (x+10)+(x+10)+(x+10) cm

=( 3x+30 ) cm

According to the question :-

(3x+30):3x =5:4

⇒15x=12x+120

⇒15x-12x=120

⇒3x=120

⇒x=40

• Each side of the given triangle = 40 cm

Perimeter of the given triangle,

= (40+40+40 ) cm

=120 cm

Trerefore the perimeter of the given triangle is 120 cm.

Answer 2

$\bf{\underline{Question:-}}$

Each side of a triangle is increased by 10 cm. If the ratio of the perimeters of the new triangle and the given triangle is 5:4, find the perimeter of the given triangle.

$\bf{\underline{Solution:-}}$

Let,

• each side be x

• perimeter of the triangle= 3x

• New perimeter = 3x + 30

therefore,

→ 3x + 30 : 3x = 5 : 4

$\sf → \large\frac{3x+30}{3x} = \frac{5}{4}$

→ 12x + 120 = 15x

→ 120 = 15x - 12x

→ 120 = 3x

→ 120/3 = x

→ 40 = x

• perimeter of given tringle = 3x
• 3 × 40 = 120cm