The perimeter of the rectangle is 28 cm, the length of one of its sides is 11 cm. Find the area of the rectangle.

univerkov | March 24, 2021 | education

1) Find the length of the second side of the rectangle, knowing the perimeter and one side. 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 and b are the sides of the rectangle.
Suppose we are given side a, we express side b from the formula for the perimeter:
P = 2a + 2b,
2b = P-2a,
b = (P-2a): 2.
Substituting the values of the perimeter and side a into the formula, we find the side b:
b = (28-2 × 11): 2 = (28-22): 2 = 6: 2 = 3 cm.
2) Find the area of the rectangle.
The area of a rectangle is the product of the lengths of its sides. Let’s write the formula for the area:
S = a × b,
S = 11 × 3 = 33 cm².
Answer: the area of the rectangle is 33 cm².

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