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.

| January 2, 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 the rectangle if its area is 1.6 times the area of the square.

We take the side of the square as x, then:
x + 5 – the length of the rectangle;
x + 3 is his side.
Since the area of the rectangle is 1.6 times the area of the square, let’s learn the equation:
(x + 5) * (x + 3) = 1.6 * x ^ 2;
x ^ 2 + 8x + 15 = 1.6 * x ^ 2;
0.6x ^ 2 – 8x -15 – 0;
x12 = (8 + – √ (64 – 4 * 0.6 * (-15)) / 1.2 = (8 + – 10) / 1.2.
x1 = (8 + 10) / 1.2 = 180/12 = 15; x2 = (8 – 10) / 1,2 – the root has no practical meaning.
The sides of the rectangle are equal:
15 + 3 = 18;
15 + 5 = 20.
The perimeter is:
2 * (18 + 20) = 76.



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