A builder set up a wooden frame in which to pour concrete for a foundation to a house. The length of the wooden frame is 24 feet. The width is 32 feet. The diagonal is 40 feet. Which best describes the foundation? The foundation cannot be a rectangle: 24 + 32 not-equals 40. The foundation cannot be a rectangle: (24 + 32) squared not-equals 40 squared. The foundation cannot be a rectangle: StartRoot 24 squared + 23 squared EndRoot not-equals 40 squared. The foundation may be a rectangle: 24 squared + 32 squared = 40 squared.

The foundation may be a rectangle: 24 squared + 32 squared = 40 squared.

Explanation:

A rectangle is a quadrilateral (that is it has four sides). The opposite sides of a rectangle are parallel to each other. Also the opposite sides are equal to each other. The four angles of a rectangle are equal to each other and measure 90° each.

The diagonals of a rectangle bisect each other. The relationship between the length, width and diagonal of a rectangle is given by:

Diagonal² = length² + width²

Given that length = 24 feet, width = 32 feet, diagonal = 40 feet, we prove that it is rectangle using:

Diagonal² = 24² + 32²

Diagonal² = 1600

Diagonal² = 40²

Hence: 40² = 24² + 32²

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-sawyer