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

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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