what is x????..

Question

Answer 1

The triangles are similar, which means they have identical angles, similar sides, and identical ratios between similar sides.

EF and BC are similar sides, and so are BA and ED. The ratio of BA to BC is the same as the ratio of ED to EF, so we can set up a proportion:

BA/BC = ED/EF

(2x - 6)/28 = (x+11)/16

Cross-multiply:

16(2x - 6) = 28(x + 11)

Distribute:

32x - 96 = 28x + 308

Combine like terms:

32x - 28x = 308 + 96

4x = 404

Isolate x by dividing both sides by 4:

x = 101

Let's make sure this agrees with our proportions:

(2x - 6)/28 = (x+11)/16

(2(101) - 6)/28 = (101+11)/16 → 7 = 7, so yes, it's correct!

Hope that helps! :)