Question 1011028
A side of a square is 2 cm greater than one of the sides of a rectangle and 5 cm smaller than the other side of the rectangle.
 Find the area of the square, if it is known, that it is 50 cm2 smaller that the area of the rectangle.
:
Let L = length of the rectangle
Let W = the width
:
"A side of a square is 2 cm greater than one of the sides of a rectangle and 5 cm smaller than the other side of the rectangle."
All side of the square is equal, therefore
L - 5 = W + 2 
L = W + 7
"The square is 50 cm2 smaller that the area of the rectangle."
L*W - (W+2)^2 = 50
Replace L with (w+7); FOIL (W+2)(W+2)
W(W+7) - (W^2 + 4W + 4) = 50
W^2 + 7W - W^2 - 4W - 4 = 50
Combine like terms
3W = 50 + 4
3W = 54
W = 54/3
W = 18 is the width of the rectangle
Then
18+2 = 20 cm is the side of the square
and
20^2 = 400 sq/cm is the area of the square