Question

найдите площадь равнобедренного треугольника АВС с основанием АС=14 см и периметром 64см.

Answer 1

Боковые стороны в равнобедренном треугольнике равны, значит боковые стороны будут равны (64-14):2 = 25. Площадь треугольника можно найти по формуле Герона.
S = корень из 32*(32-14)*(32-25)*(32-25) . Получается: корень из 32*18*7*7 = корень из 28224 = 168

Answer 2

Finding the Area of an Isosceles Triangle

To find the area of an isosceles triangle ABC with base AC = 14 cm and perimeter 64 cm, we can use the following steps:

1. Calculate the length of the sides AB and BC: - From the given perimeter, we can calculate the sum of the two equal sides, AB and BC, using the formula: perimeter = 2 * (AB + AC). - Then, we can find the lengths of AB and BC.

2. Use the Heron's formula to find the area: - Once we have the lengths of all three sides, we can use Heron's formula to find the area of the triangle.

Calculating the Length of the Sides

The perimeter of the triangle is given as 64 cm. From the perimeter, we can calculate the sum of the two equal sides, AB and BC: - 64 = 2 * (AB + 14) - AB + 14 = 32 - AB = 32 - 14 - AB = 18/2 - AB = 9 cm

So, the length of sides AB and BC is 9 cm each.

Using Heron's Formula to Find the Area

Now that we have the lengths of all three sides, we can use Heron's formula to find the area of the triangle.

Heron's formula states that the area (A) of a triangle with sides a, b, and c is given by: \[ A = \sqrt{s(s - a)(s - b)(s - c)} \] where \( s \) is the semi-perimeter of the triangle, given by: \[ s = \frac{a + b + c}{2} \]

Substituting the values: \[ s = \frac{9 + 9 + 14}{2} = 16 \]

\[ A = \sqrt{16(16 - 9)(16 - 9)(16 - 14)} \] \[ A = \sqrt{16*7*7*2} \] \[ A = \sqrt{1568} \] \[ A ≈ 39.60 \, \text{cm}^2 \]

Conclusion

The area of the isosceles triangle ABC with base AC = 14 cm and perimeter 64 cm is approximately 39.60 cm².