Answer:
Step-by-step explanation:
You want the length and width of a rectangle with perimeter 70 cm that increases in area by 50 cm² if the width is increased by 5 cm and the length is decreased by 5 cm.
Let w represent the width of the rectangle. The length can be found from ...
P = 2(L +W)
70 = 2(L +w)
35 -w = L . . . . . . divide by 2, subtract w
The area is the product of length and width, so the change in area can be represented by ...
((35 -w) -5)(w +5) -(35 -w)(w) = 50
Simplifying the above equation, we have ...
(30 -w)(w +5) -(35 -w)(w) = 50
25w -w² +150 -35w +w² = 50
100 = 10w
10 = w . . . . . width
35 -w = 35 -10 = 25 . . . . . length
The original rectangle is 25 cm long and 10 cm wide.
