The length of the triangle was reduced by 2 times, and the width was increased by 1 dcm, and a square was obtained.

The length of the triangle was reduced by 2 times, and the width was increased by 1 dcm, and a square was obtained. Find the side of the square, if the area of the rectangle is 60dtsm2?

1) If, after reducing the length and increasing the width of the triangle, a square turned out, then this triangle was originally rectangular.
2) Then we denote the long one by X * 2, and the width by X – 1 – these will be the sides of the square.
3) Substitute these values into the formula for the area of a triangle.
2 * x * (x-1) = 60.

x * (x-1) = 30.
x ^ 2 – x = 30.

x2 – x – 30 = 0.

x1 = – 5 – does not fit, x2 = 6, according to Vieta’s theorem.
Therefore, our answer is: 6 cm is the side of the square.