Question

3. Find the area of a triangle two sides of which are 15 cm
and 39 cm and the perimeter is 90 cm.​

Answer 1

Step-by-step explanation:

this is other side and area can be determined by the formula

Answer 2

Given :

• First side of Triangle = 15cm
• Second side of Triangle = 39cm
• Perimeter of Triangle = 90cm

To Find :

• Area of the Triangle

Solution :

✰ Here in this question, Two sides and perimeter of Triangle are given. So firstly we will find the third side of the triangle after that we will find the semi perimeter of the Triangle. Now after getting the third side and semi perimeter, we will apply Heron's Formula to find the area of the triangle. Let's assume the third side of the Triangle be x.

⠀

⠀⠀⠀⟼⠀⠀⠀Sum of Sides = Perimeter

⠀⠀⠀⟼⠀⠀⠀x + 15 + 39 = 90

⠀⠀⠀⟼⠀⠀⠀x + 54 = 90

⠀⠀⠀⟼⠀⠀⠀x = 90 - 54

⠀⠀⠀⟼⠀⠀⠀x = 36

⠀

Thus Third Side of Triangle is 36cm

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⠀

✰ Now, We will find the semi perimeter of the Triangular field.

⠀⠀⠀⟼⠀⠀⠀s = a + b + c/2

⠀⠀⠀⟼⠀⠀⠀s = 15 + 39 + 36/2

⠀⠀⠀⟼⠀⠀⠀s = 15 + 75/2

⠀⠀⠀⟼⠀⠀⠀s = 90/2

⠀⠀⠀⟼⠀⠀⠀s = 45cm

⠀

Thus semi perimeter of Triangle is 45cm

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⠀

✰ Now, We will find the area of the Triangular field using Heron's Formula.

➟ √s (s - a) (s - b) (s - c)

➟ √45 (45 - 15) (45 - 39) (45 - 36)

➟ √45 × 30 × 6 × 9

➟ √1350 × 54

➟ √72900

➟ 270cm²

⠀

Thus Area of Triangle is 270cm²

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