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