Question

Знайти площу прямокутного чотирикутника, якщо його діагональ складає 10 см, а одна зі сторін - 8 см

Answer 1

Ответ:

За теоремою Піфагора знайдемо другу сторону:

$\sqrt{10^{2}-8^{2} }$=$\sqrt{100-64}$=$\sqrt{36}$=6 (см)

S=ab

S=8*6=48 (см²)

Answer 2

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To find the area of a rectangle, you need to know the length and width of the rectangle. If you only know the diagonal and one side, you can use the Pythagorean theorem to find the other side. The Pythagorean theorem states that $$a^2 + b^2 = c^2$$, where $$a$$ and $$b$$ are the legs of a right triangle and $$c$$ is the hypotenuse. In this case, the diagonal of the rectangle is the hypotenuse and the sides are the legs.

Let $$x$$ be the unknown side of the rectangle. Then we have $$x^2 + 8^2 = 10^2$$, which simplifies to $$x^2 = 36$$. Taking the square root of both sides, we get $$x = 6$$ or $$x = -6$$. Since the side of a rectangle cannot be negative, we choose the positive value. Therefore, the other side of the rectangle is 6 cm.

The area of a rectangle is given by the formula $$A = lw$$, where $$l$$ is the length and $$w$$ is the width. In this case, we have $$A = 8 \times 6 = 48$$ cm².

The answer is 48 cm².

Some additional information that might be useful for you are:

- A rectangle is a quadrilateral with four right angles. The opposite sides of a rectangle are parallel and equal. The diagonals of a rectangle are also equal and bisect each other. - The Pythagorean theorem is a mathematical formula that relates the lengths of the sides of a right triangle. It is named after the Greek mathematician Pythagoras, who is credited with proving it. The Pythagorean theorem is one of the most important and widely used theorems in geometry. - The square root of a number is a number that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 times 3 is 9. The symbol for the square root is $$\sqrt{}$$. There are two possible square roots for any positive number, one positive and one negative. For example, the square roots of 4 are 2 and -2. The negative square root is usually ignored when dealing with lengths or areas, since they cannot be negative.

: [1](https://ua.onlinemschool.com/math/assistance/figures_area/rectangle1/) : [2](https://yukhym.com/uk/geometriya/priamokutnyky-testovi-pryklady.html) : [3](https://naurok.com.ua/test/ploschi-chotirikutnikiv-povtorennya-306418.html)