Question

Под строительную площадку отвели участок прямоугольной формы, длина которого на 30 метров больше его ширины. При утверждении плана застройки выяснилось, что граница участка проходит по территории водоохранной зоны, поэтому его ширину уменьшили на 20 метров. Найдите длину участка, если после утверждения плана застройки площадъ участка составила 2400м в квадрате. Помогите решить срочно!

Answer 1

Пусть ширина площадки - А... Тогда из условия видно, что площадку сначало увеличили на 30, а потом уменьшели на 20 <=> B (Ширина) = А+10

По условию S = 2400, а также S = А*B =>
$2400 = A*(A+10)\\ a^no numeric noise key 1024 +10a +2400 = 0\\ a_no numeric noise key 1023 = \frac{-10б \sqrtno numeric noise key 1022}no numeric noise key 1021 = \frac{-10б 70}no numeric noise key 1020\\ \\ => 1019 =30; \ 1018 =-40$
Но растояние не может быть меньше нуля... => А = 30

=> B = 40

ОТВЕТ: 40
 

Answer 2

Problem Analysis

We are given a rectangular plot of land for construction. Initially, the length of the plot is 30 meters greater than its width. However, it was later discovered that the plot's boundary encroaches upon a water conservation zone, so the width was reduced by 20 meters. We need to find the length of the plot if the area of the plot after the approval of the construction plan is 2400 square meters.

Solution

Let's assume the width of the plot is x meters. According to the given information, the length of the plot is 30 meters greater than its width, so the length would be x + 30 meters.

After the approval of the construction plan, the width of the plot was reduced by 20 meters. Therefore, the new width would be x - 20 meters.

We know that the area of a rectangle is given by the formula: Area = Length × Width.

According to the problem, the area of the plot after the approval of the construction plan is 2400 square meters. So we can write the equation as:

2400 = (x + 30) × (x - 20)

To solve this equation, we can expand the equation and simplify it:

2400 = x^2 + 10x - 600

Now, let's solve this quadratic equation to find the value of x.

Solving the Quadratic Equation

To solve the quadratic equation, we can rearrange it in the standard form: ax^2 + bx + c = 0.

Comparing the equation x^2 + 10x - 600 = 2400 with the standard form, we have: - a = 1 - b = 10 - c = -600 - 2400 = -3000

We can use the quadratic formula to find the values of x:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values, we get:

x = (-10 ± √(10^2 - 4(1)(-3000))) / (2(1))

Simplifying further:

x = (-10 ± √(100 + 12000)) / 2

x = (-10 ± √12100) / 2

x = (-10 ± 110) / 2

Now, we have two possible values for x:

1. x = (-10 + 110) / 2 = 100 / 2 = 50 2. x = (-10 - 110) / 2 = -120 / 2 = -60

Since the width of a plot cannot be negative, we can discard the second solution.

Therefore, the width of the plot is 50 meters.

To find the length of the plot, we can substitute this value back into the equation length = width + 30:

length = 50 + 30 = 80 meters

So, the length of the plot is 80 meters.

Answer

The length of the plot is 80 meters.