Question

Прямоугольный участок с размерами 141 и 86 м заменили другим участком той же площади, у которого длинна больше ширины на 35 м. найти измерения другого участка без икса.

Answer 1

площадь участка=141*86=12126

пусть х----------длина нового участка

х-35--------------ширина нового участка

х*(х-35)=12126

х²-35х-12126=0

Д=1225-4*(-12126)=49729

х₁=(35+223)/2=129

х₂=(35-223)/2  нет смысла

129-35=94

 

другой участок имеет размерность  129Х94

 

 

Answer 2

Finding the Dimensions of the New Plot

To find the dimensions of the new plot, we can set up an equation based on the given information. Let's denote the width of the new plot as w and the length as l.

According to the problem, the new plot has the same area as the original plot, which is 141 m * 86 m. Therefore, we can write the equation:

w * l = 141 * 86 We also know that the length of the new plot is 35 m longer than its width:

l = w + 35

Now we can substitute the value of l in terms of w into the equation above:

w * (w + 35) = 141 * 86

Simplifying this equation will allow us to find the dimensions of the new plot.

Let's solve this equation step by step:

1. Expand the equation:

w^2 + 35w = 141 * 86

2. Rearrange the equation to bring all terms to one side:

w^2 + 35w - 141 * 86 = 0

3. Solve the quadratic equation. We can use the quadratic formula:

w = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 35, and c = -141 * 86.

4. Substitute the values into the quadratic formula:

w = (-35 ± √(35^2 - 4 * 1 * (-141 * 86))) / (2 * 1)

5. Simplify the equation:

w = (-35 ± √(1225 + 4 * 141 * 86)) / 2

w = (-35 ± √(1225 + 48456)) / 2

w = (-35 ± √49681) / 2

6. Calculate the square root:

w = (-35 ± 223) / 2

7. Solve for w:

w = (-35 + 223) / 2 or w = (-35 - 223) / 2

w = 188 / 2 or w = -258 / 2

w = 94 or w = -129

Since the width cannot be negative, we discard the negative solution.

Therefore, the width of the new plot is 94 m.

8. Substitute the value of w into the equation l = w + 35 to find the length:

l = 94 + 35

l = 129 m

Therefore, the dimensions of the new plot are 94 m by 129 m.