book Maths Puzzle Numerical Ability

There is the square ABCD. Trace a line between corner A and midpoint E of side DC. Trace another line between corner A and point F of side DC such that AF equals AB+FC. Prove that angle DAE is half of angle FAB.

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i'm not sure if this is the right category i im learning primeter and i am not sure what im doing here's an example of 1 of my problems i just need to no how it gets worked out the The perimeter of a rectangle is 34 feet, and the diagonal is 13 feet long. What are the length and width of the rectangle?