Question

1. If the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square, the area of which will be 40 cm2 greater than the area of the rectangle. Find the area of the rectangle.
2.The perimeter of a rectangle is 30 cm. If its length is decreased by 3 cm and its width is increased by 5 cm, the area of the rectangle will decrease by 8 cm2. Find the area of the original rectangle.

Answer 1

Let L be length, W be width
(L-4)=(W+5)
(L-4)(W+5)=LW+40
simplify the first equation: L-W=5

simplify the second equation: (L-4)(W+5)=LW+40
               LW-4W+5L-20=LW+40  =>5L-4W=60
             
solve this system of equations: L-W=9
                                                  5L-4W=60
you get W=15, L=24, so the area is 24*15=360

#3:
(L-3)(W+5)=LW-8
2L=2W=30
W=68/8=8.5, L=52/8=6.5, LW=55.25