# The area of the rectangle is 14cm2 and the perimeter is 18cm. How do I find the dimensions of a rectangle?

December 30, 2020 | education

| Decision:

The area of a rectangle is the product of its two adjacent dimensions.

The perimeter of a rectangle is the sum of all its dimensions.

Let, u cm – one measurement

x cm – another dimension

Let’s compose a system of equations:

y * x = 14

(y + x) * 2 = 18

We solve the system of equations by the substitution method:

y * x = 14

2y + 2x = 18

y * x = 14

2y = 18-2x

y * x = 14

y = (18-2x) / 2

y * x = 14

y = 9th

(9-x) * x = 14

y = 9th

We solve the equation (9-x) * x = 14:

9x-x ^ 2 = 14

x ^ 2-9x + 14 = 0

D = 81-56 = 25

x1 = (9-5) / 2 = 4/2 = 2

x2 = (9 + 5) / 2 = 14/2 = 7

y1 = 9-2 = 7

y2 = 9-7 = 2

Answer: 2cm, 7cm

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