A student needs 5 paper triangles for some craft work such that side of the second triangle are twice the sides of the first triangle, sides of the third triangle are twice the sides of the second triangle and so on..

Find the ratio of areas of the first and the fifth triangles.

Asked by Topperlearning User | 3rd Oct, 2017, 01:32: PM

Expert Answer:

Let x cm be one side of the first triangle and then 2x cm has to be the corresponding side of the second triangle. Similarly the corresponding side of the third triangle is 4x cm, that of the fourth triangle is 8x cm and lastly the corresponding side of the fifth triangle is 16x cm.

begin mathsize 12px style So comma space fraction numerator straight A left parenthesis increment 1 right parenthesis over denominator straight A left parenthesis increment 5 right parenthesis end fraction equals fraction numerator straight x squared over denominator left parenthesis 16 straight x right parenthesis squared end fraction equals 1 over 256 end style

Answered by  | 3rd Oct, 2017, 03:32: PM