(11) Suppose you have a rectangle in front of you and a rectangular prism in front of you. Pleasejustify all responses.(a) If you triple the length and width of the rectangle, how will the area of the new rectanglecompare to the area of the original rectangle?(b) If you triple the length, width, and height of the rectangular prism, how will the surfacearea of the new rectangular prism compare to the surface area of the original rectangularprism?(c) If you triple the length, width, and height of the rectangular prism, how will the volumeof the new rectangular prism compare to the volume of the original rectangular prism?

Given that, There is a rectangle and a rectangular prism in front of you. Ans we have to find the answer of given question.Ans (a). Let the length of the rectangle is L and width of the rectangle is W. Then the area of the rectangle is, A = LW Now according to the question, triple the length and width of the rectangle,then new area will be, A' = 3L × 3W A' = 9LW A' = 9A Thus new area is the the 9 times of old area. ..............Answer Ans (b). Let the length, width and hieght of the rectangular prism are L, W and H respectfully. Then surface area of the rectangular prism will be, A = 2(WL + HL + HW) Now according to the question triple the length, width and hieght, then new surface area will be, A' = 2(3W×3L + 3H×3L + 3H×3W) A' = 2(9WL + 9HL + 9HW) A' = 18(WL + HL + HW) A' = 9A Thus new surface area is the the 9 times of old surface area. ..............Answer Ans (c). Let the length, width and hieght of the rectangular prism are L, W and H respectfully. Then volume of the rectangular prism will be, V = WHL Now according to the question triple the length, width and hieght, then new volume will be, V' = 3W×3H×3L V' = 27WHL V' = 27V Thus new volume is the the 27 times of old volume. ..............Answer