Question

Катети прямокутного трикутника відносяться як 5:12 а периметр дорівнює 90 см. Знайти гіпотенузу.

Answer 1

$\sqrt{(12x)^2+(5x)^2}=\sqrt{144x^2+25x^2}=\sqrt{169x^2}=13x$
Все стороны треугольника относятся как 5:12:13
P=90
P=5x+12x+13x
90=30x
x=3
Длина гипотенузы => 3*13=39 см

Answer 2

Finding the Hypotenuse of a Right-Angled Triangle

To find the hypotenuse of a right-angled triangle when the ratio of the legs is given, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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.

Given: - The ratio of the legs: 5:12 - The perimeter: 90 cm

Calculating the Lengths of the Legs

We can start by expressing the ratio of the legs as 5x and 12x, where x is a common multiplier. This allows us to find the actual lengths of the legs.

Using the given perimeter of 90 cm, we can set up the equation: 5x + 12x + hypotenuse = 90

Solving for x: 5x + 12x + hypotenuse = 90 17x + hypotenuse = 90 hypotenuse = 90 - 17x

Applying the Pythagorean Theorem

Now, we can apply the Pythagorean theorem to find the length of the hypotenuse.

The Pythagorean theorem states: hypotenuse^2 = (5x)^2 + (12x)^2

Substituting the value of hypotenuse: (90 - 17x)^2 = (5x)^2 + (12x)^2

Solving this equation will give us the value of x, which can then be used to find the length of the hypotenuse.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.