The length of a rectangular piece of cardboard is 2 cm greater than its width. If the length and the width were each decreased by 1 cm, the area of the cardboard would be decreased by 27 cm². What are the dimensions of the original piece of cardboard? Write and solve an equation to represent the problem.

9514 1404 393

  13 cm wide;  15 cm long

Step-by-step explanation:

Let w represent the original width. Then the original length is (w+2) and the original area is w(w+2). After the decrease, the width is (w-1) and the length is (w+1). The decreased area is (w-1)(w+1). The difference between these areas is 27, so we have ...

  w(w+2) -(w-1)(w+1) = 27

 w^2 +2w -(w^2 -1) = 27

 2w +1 = 27

  w = (27-1)/2 = 13

The original piece of cardboard was 13 cm wide and 15 cm long.

215.92 dollars is the answer

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.