How can you tell whether a square root of a whole number is rational or rational

1. what is the measure of ∠abc? what is the measure of ∠abd?

Need an artist designed a badge for a school club. figure abcd on the coordinate grid below shows the shape of the badge: the badge is enlarged and plotted on the coordinate grid as figure jklm with point j located at (2, -2) and point m is located at (5, 4). which of these could be the coordinates for point l? a. (2, 4) b. (8, 4) c. (5, 1) d. (5, 7)

Can you me find the missing length. i attached an image.