Use differentials to determine by approximately what percentage does the area of a square table increase if its diagonal is increased from 38 centimetres to 39.235 centimetres.

Question

I know that the surface is A = 1/2y^2 and y = x * square root of 2 but I don't know how to solve it... Can someone help?

Answer 1

A = 1/2 y^2
dA = y dy ≈ y ∆y = 38 * 1.235 = 46.93
check:
1/2 * 39.235^2 - 1/2 * 38^2 = 47.69

Answer 2

so what would the answer be?,