Question

Периметри прямокутного трикутника дорівнює 13см,один із його катетів 8 см. Знайти другий катет трикутника та його гіпотенузу​

Answer 1

ΔАВС, ∠С=90°,Р=13см , АС=8см

Найти ВС, АВ

Решение

АС+ВС+АВ=13,  8+ВС+АВ=13, ВС=5-АВ

Пифагор АС²+ВС²=АВ²

64+(5-АВ)²=АВ², 64+25-10АВ+АВ²=АВ² , 91=10АВ , АВ=9,1

ВС=5-9,1<0

В УСЛОВИИ ОШИБКА

Answer 2

Finding the Second Leg and Hypotenuse of a Right Triangle

To find the second leg and hypotenuse of a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's apply this theorem to the given information. We are given that the perimeter of the right triangle is 13 cm, and one of the legs is 8 cm.

Let's denote the second leg as x and the hypotenuse as h.

Using the Pythagorean theorem, we can set up the following equation:

x^2 + 8^2 = h^2 (Equation 1)

We also know that the perimeter of the triangle is 13 cm. The perimeter of a right triangle is the sum of the lengths of all three sides. In this case, it is the sum of the two legs and the hypotenuse:

x + 8 + h = 13 (Equation 2)

Now, we have a system of two equations (Equation 1 and Equation 2) with two unknowns (x and h). We can solve this system of equations to find the values of x and h.

Let's solve the system of equations:

From Equation 2, we can rewrite it as:

x + h = 13 - 8 (Equation 3)

Simplifying Equation 3, we get:

x + h = 5 (Equation 4)

Now, we can solve Equation 4 for x:

x = 5 - h (Equation 5)

Substituting Equation 5 into Equation 1, we get:

(5 - h)^2 + 8^2 = h^2

Expanding and simplifying the equation, we get:

25 - 10h + h^2 + 64 = h^2

Simplifying further, we get:

89 - 10h = 0

Solving for h, we find:

h = 89 / 10

Substituting this value of h back into Equation 5, we can find x:

x = 5 - (89 / 10)

Simplifying, we get:

x = 11 / 10

Therefore, the second leg of the triangle is 11/10 cm and the hypotenuse is 89/10 cm.

Please note that the calculations have been rounded for simplicity.