Question

each side of a triangle is increased by 10cm. 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

Let each side be x
perimeter of the triangle= 3x
New perimeter= 3x+30
therefore,
3x+30:3x=5:4
(3x+30)/3x=5/4
4(3x+30)=3x(5)
12x+120=15x
120=15x-12x
=3x
120/3=x
40=x
perimeter of given tringle=3x
3(40)
=120cm

Answer 2

Given that,

Each side of a triangle is increased by 10cm.

If the ratio of new triangle and given triangle  is 5:4.

Let the side is x cm.

So, the perimeter of the triangle = 3x

New perimeter = 3x+30

We need to calculate the value of x

Using ratio of both triangle

$\dfrac{3x+30}{3x}=\dfrac{5}{4}$

$4(3x+30)=5\times3x$

$12x+120=15x$

$120=15x-12x$

$3x=120$

$x=40\ cm$

We need to calculate the perimeter of the given triangle

Using formula for given triangle

$\text{perimeter of given triangle}=3x$

Put the value of x

$\text{perimeter of given triangle}=3\times40$

$\text{perimeter of given triangle}=120\ cm$

Hence, The perimeter of the given triangle is 120 cm.