The length of the rectangle is 5 cm longer than the side of the square and its width is 3 cm longer

| August 7, 2021 | education

The length of the rectangle is 5 cm longer than the side of the square and its width is 3 cm longer than the side of the square. Find the perimeter of a rectangle if its area is 1.6 times the area of the square.

1. Let’s denote the length of the side of the square by X. Then the length of the rectangle is X + 5, and its width is X + 3.

2. The area of the rectangle is (X + 5) * (X + 3), and the area of the square is X ^ 2. By the condition of the problem
(X + 5) * (X + 3) = 1.6 * X ^ 2.

3. Let’s simplify the expression, we get the quadratic equation: 0.6 * X ^ 2 – 8 * X – 15 = 0.

4. The discriminant of the equation D ^ 2 = 64 + 36 = 100. That is, D = 10.

5. The roots of the equation are X = 15 and X = – 5/3. The negative root does not satisfy the condition of the problem; therefore, the side length of the square is X = 15 cm.

6. The perimeter of the rectangle is 2 * (X + 5) + 2 * (X + 3) = 40 + 36 = 76 cm.

Answer: the perimeter of the rectangle is 76 cm.



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