# The perimeter of the rectangle is 184 cm. Find the measurements of the rectangle knowing that

September 14, 2021 | education

| **The perimeter of the rectangle is 184 cm. Find the measurements of the rectangle knowing that if we increase half of its width by 2 cm, we will get a quarter of the length.**

The width is x cm, the height is y cm. Then, according to the condition that if we increase half of its width by 2 cm, we get a quarter of the length, we get the first equation of the system (x / 2 + 2 = y / 4). The second equation is obtained knowing the perimeter (2 * x + 2 * y = 184):

Simplifying the second equation by dividing everything by 2 we get the system:

x / 2 + 2 = y / 4

x + y = 92

From the first equation, we express x:

x = y / 2 – 4

From the second, we express x:

x = 92 – y

y / 2 – 4 = 92 – y

y = 64

x = 92 – 64

x = 28

Answer: 28 cm wide, 64 cm long.

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