Question

Один із катетів прямокутного трикутника дорівнює 9 см. Знайдіть гіпотинузу цього трикутника, якщо вона на 3 см більша за другий катет​

Answer 1

Ответ:

15 см.

Объяснение:

Нехай другий катет х см, тоді гіпотенуза х+3 см. За теоремою Піфагора

9²+х²=(х+3)²;  81+х²=х²+6х+9;  6х=81-9;  6х=72;  х=12

Другий катет 12 см, гіпотенуза 12+3=15 см.

Answer 2

Finding the Hypotenuse of a Right-Angled Triangle

To find the hypotenuse of a right-angled triangle when one of the catheti (legs) is 9 cm and the hypotenuse is 3 cm longer than the other cathetus, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's denote: - One cathetus as a (which is 9 cm in this case). - The other cathetus as b. - The hypotenuse as c (which is 3 cm longer than the second cathetus).

According to the Pythagorean theorem: c^2 = a^2 + b^2

We are given that a = 9 cm and c = b + 3.

Substituting these values into the Pythagorean theorem equation, we get: c^2 = 9^2 + b^2

And since c = b + 3, we can rewrite the equation as: (b + 3)^2 = 9^2 + b^2

Expanding and solving for b will give us the value of the second cathetus, and then we can find the hypotenuse using c = b + 3.

Let's calculate the value of b and then find the hypotenuse c.