Question

The perimeter of an isosceles triangle is 60 cm and its base is 15 cm. The area of the triangle is​

Answer 1

22.5×22.5×15

is the area

Answer 2

Given :

• Perimeter of an isosceles ∆ = 60 cm
• Base of an isosceles ∆ = 15 cm

To Find :

• Area of ∆?

Solution :

We know that in isosceles triangle two sides are equal. So,

• Let each equal side be x

Now, we know that,

• Perimeter of ∆ = Sum of all sides

Putting all values,

➡ x + x + 15 = 60

➡ 2x + 15 = 60

➡ 2x = 60 - 15

➡ 2x = 45

➡ x = 45/2

➡ x = 22.5 cm

Hence, each equal side of ∆ is 22.5 cm.

Now, finding its semi perimeter. We know that it is given by,

• s = (a + b + c)/2

Putting all values,

➡ s = (22.5 + 22.5 + 15)/2

➡ s = (45 + 15)/2

➡ s = 60/2

➡ s = 30

Hence, semi perimeter of ∆ is 30 cm.

Now, finding its area. We know that according to heron's formula area of ∆ is given by,

• A = √[s(s - a)(s - b)(s - c)]

Putting all values,

➡ A = √[30(30 - 22.5)(30 - 22.5)(30 - 15)]

➡ A = √[30(7.5)(7.5)(15)]

➡ A = √(30 × 7.5 × 7.5 × 15)

➡ A = 7.5 × √(3 × 2 × 5 × 3 × 5)

➡ A = 7.5 × √(3 × 3 × 5 × 5 × 2)

➡ A = 7.5 × 3 × 5 × √2

• Put √2 = 1.42

➡ A = 7.5 × 15 × 1.42

➡ A = 112.5 × 1.42

➡ A = 159.75

➡ A ≈ 159 cm²

Hence, area of ∆ is 159 cm² (approx).

Learn More :

• Perimeter of any figure is calculated by sum of its all sides.
• Perimeter of square = 4 × side
• Area of square = (side)²
• Perimeter of equilateral ∆ = 3 × side
• Area of equilateral ∆ = √3/4 (side)²
• Perimeter of rhombus = 4 × side
• Area of rhombus = ½ × d₁ × d₂
• Perimeter of circle = 2πr
• Area of circle = πr²
• Perimeter of rectangle = 2(l + b)
• Area of rectangle = l × b

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