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.

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)

Answer 1

Each triangle's hypotenuse is the original square's side (4). When the four triangles are glued around that central square, the rhombus's diagonals are each 8, so half-diagonals are 4. Using the Pythagorean Theorem on half-diagonals:

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