Question

Участок прямоугольника формы примыкает к дому, длина которого 10м. С трёх сторон участок обнесён изгородью длиной 130м. Чему равна площадь этого участка ?

Answer 1

Раз у прямоугольника все противоположные стороны равны значит  длина которая обнесена изгородью тоже равна 10 м. 
1.) 130 - 10 = 120 м. - ширина изгороди.
2.) 120:2 = 60 м. - ширина.
S= 60 * 10 = 600 м. в квадрате.
Ответ: S равна 600 метров в квадрате.

Answer 2

Calculation of the Area of the Plot

To calculate the area of the plot, we need to determine the dimensions of the rectangle. We know that the plot is rectangular in shape and is adjacent to a house with a length of 10 meters. The plot is enclosed by a fence on three sides, with a total length of 130 meters.

Let's assume that the width of the plot is x meters. Therefore, the length of the plot will be 10 + x meters.

To find the area of the plot, we can use the formula for the area of a rectangle: Area = Length × Width.

Substituting the values, we have:

Area = (10 + x) × x

Simplifying the equation, we get:

Area = 10x + x^2

Now, let's solve for the value of x to find the width of the plot.

Solving for the Width of the Plot

To find the width of the plot, we need to solve the equation 10x + x^2 = 130.

By rearranging the equation, we have:

x^2 + 10x - 130 = 0

We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula to find the value of x.

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, a = 1, b = 10, and c = -130.

Substituting these values into the quadratic formula, we get:

x = (-10 ± √(10^2 - 4(1)(-130))) / (2(1))

Simplifying further, we have:

x = (-10 ± √(100 + 520)) / 2

x = (-10 ± √620) / 2

Calculating the square root of 620, we get:

√620 ≈ 24.9

Substituting this value into the equation, we have:

x = (-10 ± 24.9) / 2

Now, let's calculate the two possible values of x:

1. x = (-10 + 24.9) / 2 ≈ 7.45 2. x = (-10 - 24.9) / 2 ≈ -17.45

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

Therefore, the width of the plot is approximately 7.45 meters.

Calculation of the Area of the Plot (Continued)

Now that we have the width of the plot, we can calculate the area using the formula:

Area = (10 + x) × x

Substituting the value of x into the equation, we have:

Area = (10 + 7.45) × 7.45

Calculating further, we get:

Area ≈ 17.45 × 7.45 ≈ 129.77

Therefore, the approximate area of the plot is 129.77 square meters.

Please note that these calculations are approximate and may vary slightly depending on the exact values used.