The ratio of the lengths of the sides of △abc is 3: 4: 6. the perimeter of the triangle whose vertices are the midpoints of the sides of △abc is 13 cm. find the lengths of the sides of △abc.

Given ratio of the triangle is 3:4:6

The perimeter of the triangle whose vertices are the midpoints of the sides of △ABC is 13 cm. This is the smaller triangle built within the bigger one.  

And the perimeter of the small triangle is 13 cm. The sides are midpoints of the bigger triangle so they are half the lengths of sides.

So, the bigger triangle has sides 6,8 and 12 cm.

Hence, 3+4+6 = 13. So 3*2 , 4*2 , 6*2  is the bigger one.

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