Question

Peter is making an "x marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides of 121212 centimeters. He will make the "x" by stretching red ribbon diagonally from corner to corner. How many centimeters of ribbon will peter need to make the "x"? round your answer to the nearest centimeter. Centimeters.

Answer 1

34 cm

Explanation:

You want the sum of the lengths of the diagonals of a square 12 cm on each side.

Diagonal length

The diagonal of a 12 cm square will be ...

d = √(12² +12²) = 12√(1 +1) = 12√2

The length of the two diagonals will be ...

2d = 2(12√2) = 24√2 ≈ 33.94 . . . . . cm

Peter will need about 34 cm of ribbon to make the X on his flag.

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Additional comment

The length is found using the Pythagorean theorem, which tells you the square of the hypotenuse of a right triangle is the sum of the squares of its legs. It is useful to remember that the hypotenuse of an isosceles right triangle is √2 times the leg length. The diagonal of a square divides it into two isosceles right triangles.

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