# The perimeter of the rectangle is 30 cm, one of its sides is 3 cm larger than the other, find the sides and area of the rectangle.

July 29, 2021 | education

| To solve this problem, recall the formula for the area of a rectangle. The area of the rectangle is equal to the product of the length and the width. S = a * b, where a is the length and b is the width. The perimeter of a rectangle is the sum of the lengths of all its sides. Since in a rectangle the opposite sides are equal, then P = 2 * (a + b), where a is the length, b is the width. Let the width of the rectangle be -x, then the length of the rectangle is x + 3. Knowing that the perimeter is 30cm, we will compose the equation.

2 * (x + x + 3) = 30;

2 * (2x + 3) = 30;

4x + 6 = 30;

4x = 30 – 6;

4x = 24;

x = 24/4;

x = 6.

The width is 6 cm, the length is 6 + 3 = 9 cm. Let’s calculate the area.

S = 6 * 9 = 54 sq. Cm.

Answer: 54 sq. Cm.

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