The rectangle was reduced by 2 times and the width increased by 10 cm.

| March 11, 2021 | education

The rectangle was reduced by 2 times and the width increased by 10 cm. We got a square, find the side of the square if the area of the rectangle is 60 cm2.

Let’s write the initial length of the rectangle as x and width as y.

From this it follows that the initial area of the rectangle was equal to:

x * y = 60.

Since the length was reduced by 2 times, it became equal to:

x / 2 cm.

The new width was: y + 10 cm.

We get the area:

x / 2 * (y + 10).

We express x.

x / 2 = y + 10.

x = 2 * y + 20.

Substitute the found x into the first equation.

(2 * y + 20) * y = 60.

2 * y ^ 2 + 20 * y – 60 = 0.

y ^ 2 + 10 * y – 30 = 0.

D ^ 2 = 100 + 120 = 220.

D = 14.832.

y = (-10 + 14.832) / 2 = 4.832 / 2 = 2.416 cm (width).

x = 2 * 2.415 + 20 = 24.832 cm (length).

So the length of the side of the square was:

24.832 / 2 = 12.416 cm.

Answer: 12.416 cm.



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