Question

If each side of a triangle is increased by 6 cm, the ratio of the perimeters of the resulting triangle and the original triangle is 7:4. Find the perimeter of the original triangle

Answer 1

Original triangle :-

Let each side of the triangle be x.

Perimeter = Sum of all sides

Perimeter = x + x + x = 3x

•°• Perimeter of original triangle is 3x

___________________________

New triangle :-

Each side is increased by 6cm,

So each side becomes, = (x + 6)

Perimeter = Sum of all sides

Perimeter = x+6 + x+6 + x+6

= 3x + 18

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Also,

Ratio of perimeter of new triangle and original triangle is 7:4

So,

$\frac{3x + 18}{3x} = \frac{7}{4}$

4(3x + 18) = 7(3x)

12x + 72 = 21x

72 = 21x - 12x

72 = 9x

72/9 = x

x = 8

___________________________

Each side of original triangle = x = 8cm

Perimeter of original triangle = 3x

= 3(8)

= 24

•°• Perimeter of orginal triangle is 24cm

Answer 2

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Question :

If each side of a triangle is increased by 6 cm, the ratio of the perimeters of the resulting triangle and the original triangle is 7:4 , Find the perimeter of the original triangle.

Solution :

From the question we can assume the required triangle to be a equilateral triangle.

Hence,

Innitial Perimeter Of Triangle :

Innitial Perimeter Of the triangle is equal to x + x + x and is thereby equal to 3x.

Now each side is increased by 6 cm.

Each side of the new triangle is equal to x + 6 cm.

Final Perimeter Of Triangle :

Final Perimeter Of the triangle is equal to x + x + x + 18and is thereby equal to 3x + 18 and is equal to 3 (x + 6 ) cm.

Now the ratio of the perimeters of the resulting triangle and the original triangle is 7 : 4

Hence :

$\tt{ \purple { \implies{ \dfrac{3x}{3(x + 6)} = \dfrac{7}{4} }}} \\ \\ = > 7x + 42 = 4x \\ \\ = > x = 8 \: cm.$

Perimeter of Original Triangle = 3x = 24 cm.