If the length of the side of a square is X cm
(x>3)
Extend one side by 3 cm and shorten an adjacent side by 3 cm in order to obtain a rectangle.
Express the area of the rectangle using x.
If the length of the side of a square is X cm
(x>3)
Extend one side by 3 cm and shorten an adjacent side by 3 cm in order to obtain a rectangle.
Express the area of the rectangle using x.
First, let's recall the formula for calculating the area of a rectangle:
The area of a rectangle (which has two pairs of equal opposite sides and all angles are ) with sides of length units, is given by the formula:
(square units)
With this is mind, let's proceed to solve the problem:
Calculate the area of the rectangle whose vertices we'll mark with letters
We are told that one side of the rectangle is obtained by extending one side of the square with side length (cm) by 3 cm, and the second side of the rectangle is obtained by shortening the adjacent side of the given square by 3 cm:
Therefore, the lengths of the rectangle's sides are:
cm,
Apply the above formula in order to calculate the area of the rectangle that was formed from the square as described in the question:
(sq cm)
Continue to simplify the expression that we obtained for the rectangle's area, using the difference of squares formula:
The area of the rectangle using the above formula is as follows:
(sq cm)
Therefore, the correct answer is answer C.