# The length of the rectum is 6 cm longer than its width. If the length is reduced by 2 cm, and the width by – 10 cm

The length of the rectum is 6 cm longer than its width. If the length is reduced by 2 cm, and the width by – 10 cm, then the area of the rectangle will decrease by 184 cm2. Find the length and width of the rectangle.

Let’s make an equation. Let the width be x, then the length is x + 6 cm.
We set the area of this rectangle with the letter y, to find the area of the rectangle, you need to multiply the width by the length, you get x * (x + 6) = y.
Reduce the length by 2 cm, then x + 4
Reduce the width by 10 cm, then x – 10
If we subtract the first equation from the second, then the area will decrease by 184
x * (x + 6) – (x + 4) * (x – 10) = 184
x ^ 2 + 6x – x ^ 2 + 10x – 4x + 40 = 184
12x = 144
x = 12, this is the width
12 + 6 = 18, this is the length
Area 12 * 18 = 216 cm square
Answer: width 12 cm, length 18 cm, area 216 cm

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