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 ?

Applying the properties of a square and an isosceles triangle, the perimeter of the square is: 12√2 in.

Since two sides of an isosceles triangle are equal, the diagram below shows the square that will be formed.

Using Pythagorean Theorem, the length of the side of the square, "a", would be:

a = √(3² + 3²)

a = √18 = 3√2

Perimeter of the square = 4(3√2)

Perimeter = 12√2 in.

In summary, applying the properties of a square and an isosceles triangle, the perimeter of the square is: 12√2 in.

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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)

answer: 12

step-by-step explanation:

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