Question

Стороны треугольника относиться как 5:12:13 . Найдите его площадь , если меньшая сторона равна 10. Срочно!!!

Answer 1

Стороны 10,24 и 26
Р=10+24+26=60 периметр
р=30 полупериметр

$S= \sqrt{p(p-a)(p-b)(p-c)} = \sqrt{30*20*6*4} = \sqrt{6*100*6*4}= \\ \\ 6*10*2=120$

Answer 2

Finding the Area of a Triangle

To find the area of a triangle when the sides are in the ratio 5:12:13 and the smallest side is 10, we can use Heron's formula. Heron's formula states that the area of a triangle with sides of length a, b, and c is given by:

Area = √(s(s-a)(s-b)(s-c))

Where s is the semi-perimeter of the triangle, given by:

s = (a + b + c) / 2

Let's calculate the area using these formulas.

Calculating the Area

Given that the sides of the triangle are in the ratio 5:12:13 and the smallest side is 10, we can calculate the lengths of the other two sides as follows: - If the smallest side is 10, then the sides are in the ratio 5:12:13, so the other two sides are 24 and 26.

Now, we can calculate the semi-perimeter (s) using the formula: s = (a + b + c) / 2

Substitute the values: s = (10 + 24 + 26) / 2 = 60 / 2 = 30

Now, we can calculate the area using Heron's formula: Area = √(s(s-a)(s-b)(s-c))

Substitute the values: Area = √(30(30-10)(30-24)(30-26)) Area = √(30*20*6*4) Area = √(7200) Area ≈ 84.85 square units

So, the area of the triangle is approximately 84.85 square units.