SOLUTION: 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

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.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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

RELATED QUESTIONS
The side of a square is 3 cm smaller than one of the sides of a rectangle and 2 cm... (answered by ankor@dixie-net.com)

The side of a square is 3 cm smaller than one of the sides of a rectangle and 2 cm... (answered by josmiceli)

The side of a square is 3 cm smaller than one of the sides of a rectangle and 2 cm... (answered by jorel1380)

The perimeter of a rectangle is 22 cm. One side is 5 cm longer than the other side. Find (answered by shweta)

perimeter of a rectangle is 34 cm. One side is 7 cm longer than the other side. what is... (answered by ewatrrr)

The Perimeter of a rectangle is 42 cm. One side is 9 cm longer than the other side.... (answered by stanbon)

the perimeter of a rectangle is 44 cm. one side is 12 cm longer than the other side. find (answered by blwinbbbles)

The Perimeter of a rectangle is 56 cm. One side is 12 cm longer than the other side. Find (answered by math_helper)

The length of one side of a rectangle is 5 cm longer than the other side if the perimeter (answered by Boreal)