Question

In traingle PQR and traingle ABC are equilateral traingle Area of traingle ABC = A of PQR =1/6 and AB =2 then length PQ =??
plzzz send fast guys​

Answer 1

Answer:

Since, both are equilateral triangles, then clearly both are similar triangles. So, the sides ratios are equal.

Hence, AB/PQ = BC/QR = AC/PR

Also, AB = BC = AC = 2cm

Now, area of equilateral triangle ABC = root3. a^2/4

Where a is the side of an equilateral triangle.

So, given, (root3. BC^2/4)/(root3. QR^2/4) = 1/6

=> (BC/QR) ^2 = 1/6

=> (2/QR)^2 = 1/6

=> QR = 2root6

Hence, PQ = QR = PR = 2root6 cm

If only AB/PQ = 1/6

Then, PQ = 3cm

Take the one that's correct.