# 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.