A. Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 15 ft by 9 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way. b. Suppose that in part (a) the original piece of cardboard is a square with sides of length s. Find the volume of the largest box that can be formed in this way.

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answer: the prove is mentioned below.

step-by-step explanation:

an isometric rigid transformation is a transformation of the plane that preserves lengths and angles.    

that is, the pre-image and the image under a rigid transformation will be congruent.

here, given: cb ║ ed and cb ≅ ed

prove that: δ cbf ≅ δ edf

since, cb ║ ed

therefore, by the alternative interior angle theorem,

∠fcb ≅ ∠fed

∠fbc ≅ ∠ fde

and, cb ≅ ed ( given)

therefore, the angles and sides are persevered after transformation.

thus, by the definition of isometric rigid transformation,

δ cbf ≅ δ edf