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

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

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