A square and a rectangle have equal perimeters. If a side of the square is 12 and the base of the rectangle is 19, which of the following is true

Question

.
The area of the rectangle is 35 units longer than the area of the square.
B.
The area of the rectangle is 7 times larger than the area of the square.
C.
The area of the square is 49 units larger than the area of the rectangle.
D.
The area of the rectangle is 35 units smaller than the area of the square.
E.
The area of the square and the area of the rectangle are the same

Answer 1

(1) Given we have a square we know all side lengths (x) are equal so the perimeter would be the sum of these four sides

Perimeter of Square = x + x + x + x = 4x

(2) Because we have a rectangle we know that we will have two lengths (or bases, b) and two widths (or heights, h) of equal length

*Note a rectangle can be a square in which case the base and height are equal but since we don't know that for sure we will represent the sum of the sides as follows

Perimeter of Rectangle = b + b + h + h = 2b + 2h

(3) Next we set these perimeters equal to each other, insert the given information, and solve

4x = 2b + 2h

4(12) = 2(19) + 2h

48 = 38 + 2h

10 = 2h

h = 5

(4) With all this information available we just test the answer choices for veracity. We know the area of the square is x² and the area of the rectangle is bh, which gives us 144 and 95, respectively. Therefore, the square's area is 49 square units larger than the rectangle's leaving us with answer choice C.