The rectangle and square have the same perimeter. What is the area of the square if the sides of the rectangle are 5 cm and 9 cm.
1) Calculate the perimeter of the rectangle.
The perimeter of a rectangle is the sum of the length and width of the rectangle multiplied by 2. Let’s write the formula for the perimeter of a rectangle:
P = (a + b) × 2,
where a and b are the sides of the rectangle.
P = (5 + 9) × 2 = 14 × 2 = 28 cm.
2) Calculate the side of the square. The problem statement says that the rectangle and the square have the same perimeters. The perimeter of the rectangle is 28 cm.This means that the perimeter of the square is also 28 cm.
The perimeter of any geometric shape is the sum of the lengths of all its sides. Let’s write the formula for the perimeter of the square:
P = 4 × a,
where a is the length of the side of the square.
From the formula for the perimeter, we express the side of the square:
a = P: 4.
Let’s calculate the length of the side of the square:
a = 28: 4 = 7 cm.
3) Find the area of the square.
Let’s write the formula for the area of a square:
S = a²,
S = 7² = 49 cm².
Answer: the area of the square is 49 cm².
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