Question

Use the image to answer the question.

A square and a diamond with a square shape within it, sit side by side. The square is labeled 4 inches and has two diagonal lines in it that intersect. An arrow points left from the square to the diamond. The upper left line of the diamond is labeled x.
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For an art project, Della is cutting four equal triangles from a square piece of colored paper by cutting along the two diagonals of the square. She then creates a rhombus by gluing the four triangles in the manner shown in the image. Given that the side length of the original square is 4 inches, apply the Pythagorean Theorem to find x, the side length of the rhombus. Round the answer to two decimal places.

(1 point)
x=

inches

Answer 1

When the four triangles are glued around the central square, one side x of the rhombus is the hypotenuse of a right triangle with legs 4 and 4. By the Pythagorean Theorem,

x = sqrt(4^2 + 4^2) = sqrt(32) = 4√2 ≈ 5.66 inches.