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

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.