Question

In rhombus ABCD, the diagonals AC and BDintersect at E. If AE=5 and BE=12, what is thelength of AB?

Answer 1

Diagonals that bisect each other are perpendicular and form a right angle.

AEB is a right triangle.

We can apply the Pythagorean theorem:

c^2 = a^2+b^2

Where c is the hypotenuse (longest side) and a and b the other 2 legs.

Replacing:

AB^2 = AE^2+BE^2

AB^2 = 5^2+12^2

AB^2 = 25+144

AB^2 = 169

AB=√169 = 13

Lenght of AB= 13