# The perimeter of the rectangle is 30cm. find its sides if you know that the area of the rectangle is 56 cm2.

June 29, 2021 | education

| perimeter of the rectangle = 30 cm

area of a rectangle = 56 cm squared

based on rectangle formulas

perimeter = 2 * (length + width)

area = length * width,

find the value of the length and width

let x be the length of the rectangle, that is, one side of the rectangle

y is the width of the rectangle, the other side, then

30 = 2 * (x + y)

56 = x * y

we obtain the system of equations

solve it and find what the sides of the rectangle are equal to

x + y = 30/2

x * y = 56

x + y = 15

x * y = 56

1) x = 15 – y

2) (15 – y) * y – 56 = 0

y squared – 15 * y + 56 = 0

hence y = 7

and y = 8

3) x = 15 – 7 = 5 y

x = 15 – 8 = 7

means the rectangle has sides equal to 7 cm and 8 cm

answer: the rectangle has sides equal to 7 cm and 8 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.