Question

the perimeter of an isosceles triangle is 32cm. the ratio of the equal side to its base is 4:2. find the area of the triangle​

Answer 1

Answer:

Perimeter of the isosceles triangle is equal to the sum of all sides of the triangle. Consider an isosceles triangle △ABC in which AB=AC are equal sides and BC is a base. Given, the perimeter of an isosceles triangle is 32cm and the ratio of the equal sides to its base is 3:2.

Answer 2

Given :

• The ratio of side = 4:2
• Perimeter = 32 cm

To find :

• the area of the triangle

Solution :

⇒ Let's find the measure of sides.

4x + 4x + 2x = 32 cm

              10x = 32 cm

                  x = 32/10

                  x = 3.2 cm

4x = 3.2 × 4

    = 12.8 cm

4x = 3.2 × 4

    = 12.8 cm

2x = 3.2 × 2

    = 6.4 cm

⇒ Next, let's find the Semi-Perimeter.

Semi-Perimeter = a + b + c/2

                          = 12.8 + 12.8 + 6.4/2

                          = 32/2

                          = 16 cm

⇒ Now, let's find the Area of Triangle using "Heron's Formula".

Heron's formula = √s(s - a) (s - b) (s - c)

                           = √16(16 - 12.8) (16 - 12.8) (16 - 6.4)

                           = √16 (3.2) (3.2) (9.6)

                           = √16 × (3.2) × (3.2) × (9.6)

                           = √1572.864

• Therefore, the area of the isoceles triangle is √1572.864 cm².