1.

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»

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


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