# The diagonal of the rectangle is 6 cm larger than one side and 3 more than the other. Find the sides of the rectangle.

August 22, 2021 | education

| It is known that the diagonal of a rectangle is 6 and 3 centimeters longer than its width and length, respectively.

Let’s designate the diagonal as “a” cm, then the width and length will be equal to “a – 6” and “a – 3” cm.

Using the Pythagorean theorem, we compose the equation:

a² = (a – 6) ² + (a – 3) ²;

a² = a² – 12a + 36 + a² – 6a + 9;

a² – 18a + 45 = 0;

a = (18 + √ (18² – 4 * 45)) / 2;

a = (18 + √ (324 – 180)) / 2;

a = (18 + 12) / 2;

a = 30/2 = 15 cm, the diagonal of the rectangle.

15 – 6 = 9 cm, width.

15 – 3 = 12 cm, length.

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