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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The lines that intersect within the square create 4 triangles. The square within the diamond shape is an empty space and is created by the 4 triangles. The sides of the square are the bases of the triangles, and the 4 points of the diamond are the tips of the triangles.


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
Remaining Attempts : 3
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Answer 1

When the four congruent right triangles are glued around the central 4-inch square, two adjacent triangle tips form a right triangle with legs 4 and 4. By the Pythagorean Theorem,

x^2 = 4^2 + 4^2 = 16 + 16 = 32, so x = √32 = 4√2 ≈ 5.66 inches.

x = 5.66 inches (to two decimal places)