Question

find the area of triangle whose sides are 20 CM ,21 cm and 13 cm find the length of the altitude corresponding to the longest side​

Answer 1

Step-by-step explanation:

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Answer 2

Required Answer :

The area of triangle = 126 cm²

The length of the altitude corresponding to the longest side = 12 cm

Given :

• Sides of a triangle :
• First side = 20 cm
• Second side = 21 cm
• Third side = 13 cm

To find :

• Area of the triangle
• Length of the altitude corresponding to the longest side

Solution :

To calculate the area of the triangle, we will use the Heron's formula. For that firstly, we will calculate the semi perimeter of the triangle.

Formula to calculate the semi perimeter :

• Semi perimeter = Perimeter ÷ 2

or

• Semi perimeter = (a + b + c) ÷ 2

where,

• a, b and c denotes the three sides of the triangle

we have,

• a = 20 cm
• b = 21 cm
• c = 13 cm

⇒ Semi perimeter = (20 + 21 + 13) ÷ 2

⇒ Semi perimeter = 54 ÷ 2

⇒ Semi perimeter = 27

• Semi perimeter = 27 cm

Using formula,

• Heron's formula = √s(s - a)(s - b)(s - c)

Substituting the given values :

⇒ Area = √27(27 - 20)(27 - 21)(27 - 13)

⇒ Area = √27(7)(6)(14)

⇒ Area = √15876

⇒ Area = √126 × 126)

⇒ Area = ± 126

As we know, area of triangle cannot be negative. So, the negative sign will get rejected.

⇒ Area = ± 126 Reject -ve

⇒ Area = 126

Therefore, the area of triangle = 126 cm²

The longest side of the triangle = 21 cm

Using formula,

• Area of triangle = ½ × b × h

where,

• b = base
• h = height

Substituting the given values :

⇒ 126 = ½ × 21 × h

⇒ 126 = 21/2 = h

⇒ 126 × 2/21 = h

⇒ 12 = h

Therefore, the length of the altitude corresponding to the longest side = 12 cm