The sum of two adjacent sides of the rectangle is 27 cm. Find the sides of the rectangle

| August 17, 2021 | education

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

Let us denote the lengths of the adjacent sides of the rectangle by the letters a and b.

The sum of two adjacent sides a + b = 27.

The area of the rectangle is a * b = 180.

Let’s solve the resulting system of equations.

Substitute the value b = (27 – a) into the second equation.

a * (27 – a) = 180, open the brackets and solve the quadratic equation.

a ^ 2 – 27a + 180 = 0.

a1.2 = 1/2 * (- (-27) +/- √ (272 – 4 * 180)).

a1 = 1/2 * (27 + √ (729 – 720)) = 1/2 * (27 + √9) = 1/2 * (27 + 3) = 15.

a2 = 1/2 * (27 – 3) = 12.

With a = 15, the value b = 27 – 15 = 12, with a = 12, the value b = 27 – 12 = 15.

Answer: the lengths of the adjacent sides of the rectangle are 12 and 15 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.