When all sides of a rectangle with dimensions of 2m by 4m were increased

When all sides of a rectangle with dimensions of 2m by 4m were increased by the same length, its area increased by 3 times. Find the new dimensions of the plot.

Let’s find out how many square meters the area of the rectangle is equal to:

2 * 4 = 8.

Let’s find out how many square meters the area of the modified figure is equal to:

8 * 3 = 24.

Let us express the length by which the dimensions were increased, for which we use the variable a.

Then the new first size can be written as 2 + a, and the new second in the form of 4 + a.

Knowing the new area, we write the equation:

(2 + a) * (4 + a) = 24;

8 + 4a + 2a + a2 – 24 = 0;

a2 + 6a – 16 = 0;

D = 36 – 4 * (-16) = 100 = 102;

a1 = (-6 + 10): 2 = 2;

a2 = (-6 – 10): 2 = -8 (not suitable).

2 + 2 = 4;

2 + 4 = 6.

Answer: 4 meters and 6 meters.