# The perimeter of the rectangle is 30 cm and its area is 54 cm squared. What are the length and width of the rectangle?

December 28, 2020 | education

| 1. We take the length of the rectangle for x, for its width.

2. Let’s compose two equations:

2x + 2y = 30;

xy = 54; x = 54 / y.

3. Substitute x = 54 / y in the first equation:

108 / y + 2y = 30;

(108 + 2y ^ 2) / y = 30;

2y ^ 2 – 30y + 108 = 0;

y ^ 2 – 15y + 54 = 0;

The equation has 2 solutions.

The first value y = (15 + √15 ^ 2 – 4 x 54) / 2 = (15 + 3) / 2 = 9 cm; x = 54: 9 = 6 cm.

The second value is y = (15 – 3) / 2 = 6 cm; x = 54: 6 = 9 cm.

Answer: the length must be greater than the width, so the length of the rectangle is 9 cm, width is 6 cm.

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