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

`\textsf{Let a, b and c be the sides of the original triangle. Then, a+6, b+6 and c+6 will}\\\textsf{be the sides of the resulting triangle.}\\\\\textsf{According to the question,}`

`\sf\\\textsf{Perimeter of resulting triangle : Perimeter of original triangle = 3 : 4}`

`\textsf{or, (a+6+b+6+c+6): (a+b+c) = 7: 4}`

`\sf\\\textsf{or, }(a+b+c+18)/(a+b+c)=(7)/(4)`

`\sf\\\textsf{or, }4a+4b+4c+4(18)=7a+7b+7c\\\textsf{or, }72=3a+3b+3c\\\textsf{or, }a+b+c=24\\\therefore\ \textsf{Perimeter of the original triangle = 24cm}`