Answer:
AK ≈ 27.5
Explanation:
in a rhombus
the diagonals are perpendicular bisectors of each other, then
∠ DAK = 90° and Δ DAK is right
using Pythagoras' identity in right triangle DAK
AK² + DA² = DK²
AK² + 12² = 30²
AK² + 144 = 900 ( subtract 144 from both sides )
AK² = 756 ( take square root of both sides )
AK =
≈ 27.5 ( to the nearest tenth )