# The rectangular section with measurements of 141 and 86 m was replaced by another section of the same area

The rectangular section with measurements of 141 and 86 m was replaced by another section of the same area, whose length was 35 m greater than the width. Find the measurements of another section.

Solution:
Let x be the width of the new section, then x + 35 is the length of the new section.
Since the areas of the plots are equal, we will compose the equation:
141 * 86 = x * (x + 35);
12126 = x ^ 2 + 35x;
x ^ 2 + 35x – 12126 = 0;
D = 1225 + 4 * 12126 = 1225 + 48504 = 49729> 0 – 2 roots;
x1 = (- 35 + 223) / 2 = 94 (m) – the width is suitable;
x2 = (- 35 – 223) / 2 = – 129 – does not fit, since it is negative;
2) 94 + 35 = 129 (m) – the length of the new section;
Answer: 94 meters and 129 meters.
Explanations. The quadratic equation is solved, for example, through the discriminant. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.