Question

один із катетів прямокутника на 8см менше гіпотинузи а другий катет дорівнює 16 см знайти пириметр трикутника​

Answer 1

Ответ:

48 см

Объяснение:

нехай гіпотинуза буде а. тоді один з катетів буде дорівнювати а-8. За теоремою Піфігора маємо рівняння:

а^2=(а-8)^2+16^2

а^2-а^2+16а=16^2+64

16а=320

а=20 - гіпотенуза

20-8=12 - другий катет

12+20+16= 48 см - периметр прямокутного трикктника

Answer 2

Given Information

We are given that one of the legs of a right triangle is 8 cm shorter than the hypotenuse, and the other leg is 16 cm long. We need to find the perimeter of the triangle.

Solution

To find the perimeter of the triangle, we need to know the lengths of all three sides. Let's denote the hypotenuse as 'c', and the two legs as 'a' and 'b'.

According to the given information, one of the legs is 8 cm shorter than the hypotenuse. So we can write the equation: a = c - 8 cm

We are also given that the other leg is 16 cm long. So we can write the equation: b = 16 cm

To find the perimeter, we need to add up the lengths of all three sides: Perimeter = a + b + c

To solve for 'c', we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: c^2 = a^2 + b^2

Substituting the values of 'a' and 'b' from the given information, we get: c^2 = (c - 8 cm)^2 + (16 cm)^2

Expanding and simplifying the equation, we get: c^2 = c^2 - 16c + 64 + 256

Simplifying further, we get: 0 = -16c + 320

Solving for 'c', we find: c = 20 cm

Now that we know the value of 'c', we can substitute it back into the equation for 'a': a = c - 8 cm a = 20 cm - 8 cm a = 12 cm

So the lengths of the sides of the triangle are: a = 12 cm b = 16 cm c = 20 cm

Now we can calculate the perimeter: Perimeter = a + b + c Perimeter = 12 cm + 16 cm + 20 cm Perimeter = 48 cm

Therefore, the perimeter of the triangle is 48 cm.

Conclusion

The perimeter of the triangle with one leg 8 cm shorter than the hypotenuse and the other leg measuring 16 cm is 48 cm.