Question

the perimeter of the Isoleces triangle is 32. the ratio of the equal side to its base is 3:2 find the area of the triangle​

Answer 1

Given:

• Perimeter of isosceles triangle is 32 cm.
• Ratio of equal sides to base = 3 : 2

To Find:

• Area of triangle

Solution:

Let the equal side = 3x

So, base = 2x

★ Perimeter of the triangle = 32

⇒ 3x + 3x + 2x = 32

⇒ 8x = 32

⇒ x = 4.

Then,

• Equal side = 3x = 3×4 = 12
• Base = 2x = 2×4 = 8

The sides of the triangle = 12cm, 12cm and 8cm.

Let a = 12, b = 12, c = 8

★ s = (a + b + c)/2

→ s = (12 + 12 + 8)/2

→ 32/2

→ 16.

★Area of the triangle = √s(s - a)(s - b)(s - c)

→ √16(16 - 12)(16 - 12)(16 - 8)

→ √16 × 4 × 4 × 8

→ 32√2 cm²

Hence,

• Area of triangle = 32√2cm²