I would explain it this way:
Say W is the Width and H is the Height in inches…
- We know that the resolution is 1366x768 and therefore w ÷ h = 1366 ÷ 768 = W ÷ H = 1.77865
2. We know that the diagonal is 10.6 inches. That is: SQR(W^2+H^2) = 10.6 inches.
a) from 1) we get W = 1.77865 * H.
b) from 2) and a) we get SQR((1.77865*H)^2 + H^2) = 10.6
c) from b) we get SQR(3.16358 * H^2 + H^2) = 10.6
d) from c) we get SQR(4.16358 * H^2) = 10.6
e) from d) we get SQR(4.16358) * SQR(H^2) = 10.6
f) from e) we get 2.040485 * H = 10.6
g) from f) we get H = 10.6 ÷ 2.040485 = 5.195 inches
h) From a) and g) we have: W = 1.77865 * H = 1.77865 * 5.195 = 9.24 inches
So the W x H is 9.24 x 5.195 inches.