Question

Сторони трикутника дорівнюють 4; 13;15. Знайти меншу висоту трикутника.​

Answer 1

Обчислимо площу трикутника за формулою Герона. піврериметр Даного трикутника р=0,5(4+13+15)=16 дм.
S=√р(р-а)(р-b)(р-с)=√16(16-4)(16-13)(16-15)=√16·12·3·1=4·6=24.
h=S/4=24/4=6 дм.

Answer 2

Finding the Smallest Height of a Triangle

To find the smallest height of a triangle, we can use the formula:

Area = (base * height) / 2

Given that the sides of the triangle are 4, 13, and 15, we need to determine the base and height of the triangle.

Let's assume that the side of length 4 is the base of the triangle. We can use the formula for the area of a triangle to find the height:

Area = (4 * height) / 2

Since we know the area of the triangle, we can substitute the values into the formula and solve for the height:

Area = (4 * height) / 2

To find the area of the triangle, we can use Heron's formula:

Area = sqrt(s * (s - a) * (s - b) * (s - c))

where s is the semiperimeter of the triangle, and a, b, and c are the lengths of the sides.

In this case, the lengths of the sides are 4, 13, and 15. The semiperimeter can be calculated as:

s = (a + b + c) / 2

Substituting the values, we get:

s = (4 + 13 + 15) / 2 = 16

Now, we can calculate the area using Heron's formula:

Area = sqrt(16 * (16 - 4) * (16 - 13) * (16 - 15))

Area = sqrt(16 * 12 * 3 * 1) = sqrt(576) = 24

Now that we have the area, we can substitute it back into the formula for the height:

24 = (4 * height) / 2

Simplifying the equation, we get:

24 = 2 * height

Dividing both sides by 2, we find:

height = 12

Therefore, the smallest height of the triangle is 12.