If one side of the square is reduced by 2 cm and the other by 4 cm, then its area will decrease by 7 cm. Find the side of the square.
February 11, 2021 | education
| Suppose we have a square with a side whose length is x cm.
Then the area of this square is x ^ 2 cm2.
If one side of this square is reduced by 2 cm, and the other side is reduced by 4 cm, then you get a rectangle with sides (x – 2) cm and (x – 4) cm.
The area of this rectangle will be equal to (x – 2) (x – 4) cm2.
If we compare the areas of this square and the resulting rectangle, then the area of the rectangle will be 7 cm2 less than the area of the square.
(x – 2) (x – 4) = x ^ 2 – 7.
x ^ 2 – 4x – 2x + 8 = x ^ 2 – 7.
x ^ 2 – x ^ 2 – 4x – 2x = -7 – 8.
-6x = -15.
x = (-15): (-6).
x = 2.5 (cm).
Answer: the length of the side of the square is 2.5 cm.
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