Question

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

Answer 1

Answer:

The length of AB is 13 units

Explanation:

consider the sketch of the rhombus below. A rhombus is a plane shape that has all its sides equal, but unlike a square, it is skewed at an angle.

We can notice that the right angle triangle is formed between points AEB. This is a very good indicator showing that we can apply Pythagora's theorem to solve our geometry problem here.

We are looking for the length of AB. This is the hypotenuse side of the triangle. From Pythagoras' theorem,

$AB=\sqrt{(AE)^2 +(BE)^2}$

$AB=\sqrt{5^2 +12^2} =13 units$