Question

class 10th chapter 1 similarity .1..Triangle ABC and triangle DEF are equilateral triangles. If Area of triangle ABC : Area of triangle DEF=1:2 and AB=4, Find DE... ​

Answer 1

Answer:

Step-by-step explanation:

As we all know that : If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides. This proves that the ratio of the area of two similar triangles is proportional to the squares of the corresponding sides of both the triangles.

and ΔABC ~ ΔDEF (by A.A.A as it an equilateral triangle)

so AB/DE = BC/EF = AC/DF (corresponding sides of the similar triangles are in proportion or c.s.s.t)........................equation(i)

so by the above theorem

Area of Δ ABC / Area of ΔDEF = 1/2 = corresponding sides

Area of Δ ABC / Area of ΔDEF = 1/2 = AB/DE[one of the correspondng sides , by equation (i)]

Area of Δ ABC / Area of ΔDEF = 1/2 = 4/DE [as AB = 4]

also  1/2 = AB/DE

1/2 = 4/DE

DE = 8 units

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