Question

The diagonal of square ABCD intersect at point E. If BE = 10 then which of the following represents the length of AB

Answer 1

Answer :

c = 10 radical 2

Step-by-step explanation:

10^2 + 10^2 = c^2

100 + 100 = c^2

200 = c^2

Answer 2

The length of AB of the square is represented as: 10√2.

What is a Square?

• A square has two diagonals that bisect each vertex (angle 90) and also bisect each other.
• Point of intersection of two diagonals of a square forms right angle (90).

Thus, diagonals of square ABCD will form angle 90 at point E. Therefore, a right triangle BED is formed where:

• ∅ = 45°
• AB = x (hypotenuse)
• BE = 10 (opposite)

Thus, applying sine ratio, SOH, we have:

sin 45 = 10/x

x = 10/sin 45

x = 10/1/√2 (sin 45 = 1/√2)

Rationalize

x = 10 × √2

x = 10√2

Therefore, the length of AB of the square is represented as: 10√2.

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