Question

В прямоугольном треугольнике abc (с=90) медиана cm= 8,5 а катет ac= 15 найти площадь треугольника.

Answer 1

Ответ:

60 см²

Объяснение:

Медиана, проведенная к гипотенузе, равна половине гипотенузы.

АВ=2СМ=17 см

ВС=√(17²-15²)=√(289-225)=√64=8 см.

S=1/2 * 8*15=60 см²

Answer 2

Problem Analysis

We are given a right-angled triangle ABC, where angle C is 90 degrees. We are also given that the median CM is 8.5 and the length of the cathetus AC is 15. We need to find the area of the triangle.

Solution

To find the area of the triangle, we can use the formula: Area = (1/2) * base * height.

In a right-angled triangle, the median CM is equal to half the length of the hypotenuse AB. Therefore, AB = 2 * CM.

We can find the length of AB using the Pythagorean theorem, which 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. In this case, AB^2 = AC^2 + BC^2.

Let's calculate the length of AB and BC using the given information.

Calculation

Given: - CM = 8.5 - AC = 15

Using the Pythagorean theorem, we can find the length of AB: AB^2 = AC^2 + BC^2

Since angle C is 90 degrees, BC is the other cathetus of the triangle. Therefore, BC = AC.

Substituting the values, we have: AB^2 = 15^2 + 15^2 AB^2 = 225 + 225 AB^2 = 450 AB = √450

Now, we can calculate the area of the triangle using the formula: Area = (1/2) * AB * AC

Substituting the values, we have: Area = (1/2) * √450 * 15

Calculation Result

The area of the triangle is approximately 95.85 square units.

Conclusion

In a right-angled triangle ABC, with a median CM of 8.5 and a cathetus AC of 15, the area of the triangle is approximately 95.85 square units.