Question

Довжина прямокутної ділянки землі у 5 разів більша від її ширини, а площа дорівнює 980 м^2. Обчисліть довжину і ширину.

Answer 1

Пошаговое объяснение:

Длина = 5х м

Ширина = х м

S = 980 м²

5х * х = 980

5х² = 980

х² = 980 : 5

х² = 196

х1 = 14

х2 = -14

Стороны прямоугольника не могут иметь отрицательное значение, значит -14 не подходит . Остаётся : х = 14

Длина = (5х) = 5 * 14 = 70 м

Ширина = (х) = 14 м

S = 70 * 14 = 980 м²

Ответ : 70м; 14м.

Answer 2

I can help you with your math problem. Let me explain how to solve it.

The user's message is a math problem that asks to find the length and width of a rectangular plot of land, given that the length is five times the width and the area is 980 m^2. To solve this problem, we need to use the formula for the area of a rectangle, which is $$S = ab$$, where $$S$$ is the area, $$a$$ is the length, and $$b$$ is the width.

Since we know that the length is five times the width, we can write $$a = 5b$$. Substituting this into the area formula, we get $$S = 5b \times b = 5b^2$$. Now we can plug in the given value of $$S$$ and solve for $$b$$.

$$5b^2 = 980$$ $$b^2 = \frac{980}{5} = 196$$ $$b = \sqrt{196} = 14$$

We found that the width of the plot is 14 m. To find the length, we multiply the width by 5, as given in the problem.

$$a = 5b = 5 \times 14 = 70$$

We found that the length of the plot is 70 m. Therefore, the answer is:

The length of the plot is 70 m and the width is 14 m.

I hope this explanation was helpful. If you want to practice more problems like this, you can check out this online test .

Some additional information or tips:

- You can also use the quadratic formula to solve for $$b$$, but it is not necessary in this case, since the equation $$5b^2 = 980$$ has a perfect square root. - The units of the area, length, and width must be consistent. In this problem, they are all in meters, so the answer is also in meters. If they were given in different units, such as centimeters or kilometers, you would need to convert them to the same unit before applying the formula. - The area of a rectangle is one of the basic formulas in geometry. You can learn more about other geometric shapes and their formulas from this website .