The perimeter of the rectangle is the same as the perimeter of the square. What is the area of the square?
Let’s begin by considering the perimeter of the rectangle. We know that the parallel sides of a rectangle are equal in length. This means that it has two sides of length 𝑥 plus three and two sides of length two 𝑥 minus five. The perimeter of the rectangle can therefore be calculated by adding two 𝑥 minus five to 𝑥 plus three to two 𝑥 minus five and 𝑥 plus three. Collecting or grouping our like terms gives us a perimeter of six 𝑥 minus four. All four sides of a square are equal in length. This means that we can calculate the perimeter of the square by multiplying 𝑥 plus one by four.
Distributing the parentheses or expanding the brackets here, we get four multiplied by 𝑥 and four multiplied by one. This gives us a perimeter of four 𝑥 plus four. We’re told that the perimeter of the square is equal to the perimeter of the rectangle. So six 𝑥 minus four is equal to four 𝑥 plus four. We can solve this equation using the balancing method. We begin by subtracting four 𝑥 from both sides. This gives us two 𝑥 minus four is equal to four. We can then add four to both sides of this equation giving us two 𝑥 is equal to eight.
Finally, dividing both sides by two gives us a value of 𝑥 equal to four. As the sides of the square had length 𝑥 plus one, they will be equal to five as four plus one equals five. We can calculate the area of any square by squaring its length. The area of the square in this question is five squared, which equals 25. We could also calculate the area of the rectangle as it has length of seven units and width or height three units. Its area would be equal to seven multiplied by three, which equals 21. The units for area are square units.