The perimeter of rectangle WXYZ is 34 inches. A scale factor of 1.75 is used to dilate rectangle WXYZ to rectangle ABCD. What is the perimeter of rectangle ABCD?

59.5 units

Step-by-step explanation:

A rectangle is a quadrilateral (has four side) in which opposite sides are parallel and the diagonals bisect each other. The perimeter of a rectangle is:

Perimeter = 2(length + breadth) = 2(l + b)

The  perimeter of rectangle WXYZ is 34 inches. Therefore:

34 = 2(l + b)

l + b = 17

Rectangle ABCD is formed by dilating rectangle WXYZ by a scale factor of 1.75. Let l' = length of ABCD and b' = breadth of ABCD hence:

Length of ABCD = l' = 1.75l

Breadth of ABCD = b' = 1.75b

Perimeter of ABCD = 2(l' + b') = 2(1.75l + 1.75b) = 2(1.75)(l + b) = 3.5(l + b)

Perimeter of ABCD = 3.5(17) = 59.5 units