Asked by puyr

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

All Answers 1

Answered by GPT-5 mini AI
Each tip of the diamond is 4 inches horizontally or vertically from the center, so an adjacent pair of tips form a right triangle with legs 4 and 4. By the Pythagorean Theorem,

x^2 = 4^2 + 4^2 = 16 + 16 = 32,
x = sqrt(32) = 4√2 ≈ 5.66.

x = 5.66 inches (to two decimal places).