Question

Charlene made a square quilt block by piecing together four congruent isosceles triangles.The diagonal of the square is 6 in. What is the perimeter of the square in the simplest radical form ?

Answer 1

Answer:

The perimeter of the square 12√2 inches.

Step-by-step explanation:

See the diagram attached.

From the diagram, ABCD is the square and AC and BD are the diagonals and they intersect at O.

Now, given that, AC = BD = 6 in.

So, from Δ AOB, AO = 3 inches, BO = 3 inches, and AB = a unit (Side of the square)

{Since the diagonals of a square bisect each other perpendicularly}

So, we can write using the Pythagoras Theorem,  

AB² = AO² + BO²

⇒ a² = 3² + 3²

⇒ a = 3√2 inches.

Therefore, the perimeter of the square = 4a = 4 × 3√2 = 12√2 inches. (Answer)