The perimeter of a square with a side of 9.65 cm is equal to the perimeter of a rectangle

| May 6, 2021 | education

The perimeter of a square with a side of 9.65 cm is equal to the perimeter of a rectangle with a width of 8.7 cm. Find the length of the rectangle.

1) Find the perimeter of a square with a side of 9.65 cm.
A square is a quadrangle in which all sides are equal.
The perimeter of any geometric shape is the sum of the lengths of all sides. Let’s write the formula for the perimeter of the square:
P = 4 × a,
where a is the side of the square.
P = 9.65 × 4 = 38.6 cm.
2) Find the length of the rectangle.
The problem statement says that the perimeter of a square with a side of 9.65 cm is equal to the perimeter of our rectangle. We found the perimeter of the square. This means that the perimeter of the rectangle is also 38.6 cm. It turns out that we know the perimeter and width of the rectangle. So we can find the length.
The perimeter of a rectangle is the sum of the length and width of the rectangle multiplied by 2. Let’s write the formula:
P = (a + b) × 2,
where a is the length of the rectangle, b is the width.
Let us express the length of the rectangle from the formula:
P = 2a + 2b,
2a = P-2b,
a = (P-2b): 2.
Let us find a by substituting the known values ​​in the formula:
a = (38.6-2 × 8.7): 2 = (38.6-17.4): 2 = 21.2: 2 = 10.6 cm.
Answer: The length of the rectangle is 10.6 cm.



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