Question

An isosceles triangle has perimeter 24cm and each of the equal sides is 9 cm . Find the area of the triangle​

Answer 1

Answer:

Equal sides of the triangle are 9 cm each.

• Let the third side = x cm.
• Perimeter = 24 cm.

•°• 9 cm + 9 cm + x cm = 24

→ x = 24 - 9 - 9 cm

→ x = 6 cm.

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In an isosceles triangle, two sides are equal.

• a = b = 9 cm.
• c = 6 cm.

Now, semi - perimeter -

a + b + c / 2

→ 24/2

→ 12 cm.

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Therefore, Area of triangle by using heron's formula -

• √s (s-a) (s-b) (s-c)

→ √12 (12-9) (12-9) (12-6) cm²

→ √ 12 × 3 × 3 × 6 cm²

→ √2 × 2 × 3 × 3 × 3 × 2 × 3 cm²

→ √ 2² × 2 × 3² × 3² cm²

→ 2 × 3 × 3 √2 cm²

→ 18 √2 cm².

Thus, the required area of the triangle = 18 √2 cm².