Question

У прямокутному трикутнику AMB (кут M=90°) AB:AM=5:3, MB=12см. Знайдіть довжину катета АМ​

Answer 1

Ответ:

9см

Объяснение:

Тут потрібно використати теорему Піфагора

Answer 2

Finding the Length of Side AM in Right Triangle AMB

To find the length of side AM in right triangle AMB, where angle M = 90°, and AB:AM = 5:3, and MB = 12 cm, we can use the Pythagorean theorem and the given ratio of sides.

Using 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.

So, in triangle AMB, we have: - AB as the hypotenuse - AM as one of the sides - MB as the other side

The Pythagorean theorem can be expressed as: AB^2 = AM^2 + MB^2

Using the Given Ratio

We are also given that AB:AM = 5:3. This means that the ratio of the length of AB to the length of AM is 5:3.

Calculating the Length of Side AM

We can use the given ratio and the Pythagorean theorem to find the length of side AM.

First, we need to find the length of AB. Since the ratio of AB:AM is 5:3, we can express AB in terms of 3x and AM in terms of x, where x is a common multiplier.

Let's calculate the length of AB: 5x = AB

Now, we can use the Pythagorean theorem to find the value of x and then calculate the length of AM.

Calculation

Using the Pythagorean theorem: AB^2 = AM^2 + MB^2

Substituting the values: (5x)^2 = (3x)^2 + 12^2 25x^2 = 9x^2 + 144 16x^2 = 144 x^2 = 9 x = 3

Now, we can find the length of AM: AM = 3x = 3 * 3 = 9 cm

Conclusion

Therefore, the length of the side AM in the right triangle AMB is 9 cm.