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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