# One side of the rectangle is 4 times smaller than the other, and its area is equal to the area

One side of the rectangle is 4 times smaller than the other, and its area is equal to the area of a square with a side of 10 cm. Find the larger side of the rectangle.

1) Find out the area of ​​a square with a side of 10 cm. By the problem statement, this value will also be the area of ​​a rectangle: S = a ^ 2 = 10 ^ 2 = 100 (cm ^ 2);

2) Let us take for x (x) cm the value of the smaller side of the rectangle, then its larger side is (x 4) cm.

Knowing the size of the area and applying the formula for finding the area (S = a b), we compose the equation:

x * (x * 4) = 100;

x ^ 2 4 = 100;

x ^ 2 = 100: 4;

x ^ 2 = 25;

x = √25;

x1 = 5, x2 = -5.

The root of the equation x2 = -5 does not satisfy the condition of the problem, since the length of the rectangle cannot be expressed as a negative number. This means that the smaller side is 5 cm.

Find the length of the larger side: x · 5 = 4 · 5 = 20 (cm).

Answer: the large side of the rectangle is 20 cm.

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