The sum of two adjacent sides of the rectangle is 27 cm. Find the sides of the rectangle knowing that the area is 180 cm2.

1. A rectangle has two adjacent sides – this is the height and the base. Let the base be X cm, and the height Y cm.

2. Based on the condition of the problem and 1 point, X + Y = 27 cm, and X * Y = 180 cm2.

3. So X = 27 – Y.

4. Substitute the X value in the second equation. It turns out Y * (27 – Y) = 180.

5.27Y – Y2 = 180.

6.Y2 – 27Y + 180 = 0.

7. The discriminant is 9, and the roots of the equation are Y = 12 and Y = 15.

8. So X = 15 or X = 12.

9. Thus, the sides of the rectangle are 12 cm and 15 cm.