Math, asked by kv03072007, 2 months ago

A parallelogram and a triangle have the same base and equal areas. If the sides of triangle are 18 cm, 24 cm and 30 cm and their common base is 30 cm, find height of the parallelogram.​

Answers

Answered by darkdevil0047
0

Step-by-step explanation:

If the sides of triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

Answered by AestheticSoul
1

Given :

• A parallelogram and a triangle have the same base and equal areas.

• The three sides of triangle :-

  • First side = 18 cm
  • Second side = 24 cm

Third side = 30 cm

• The common base of parallelogram and triangle is 30 cm

To find :

• Height of the parallelogram

Solution :

Firstly, we will calculate the area of triangle by using the Heron's formula.

⟶ Semi perimeter of the triangle = (a + b + c) ÷ 2

where,

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

Substituting the given values :-

⟶ Semi perimeter = (18 + 24 + 30) ÷ 2

⟶ Semi perimeter = 72 ÷ 2

⟶ Semi perimeter = 36

Therefore, the semi perimeter of the triangle = 36 cm

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

where,s is the semi perimeter of the triangle

Substituting the given values :-

⟶ Area of triangle = √36(36 - 18)(36 - 24)(36 - 30)

⟶ Area of triangle = √36(18)(12)(6)

⟶ Area of triangle = √36(1296)

⟶ Area of triangle = √46,656

⟶ Area of triangle = 216

Therefore, the area of triangle = 216 cm²

⟶ Area of triangle = Area of parallelogram

Hence, Area of parallelogram = 216 cm²

Using formula,

⟶ Area of parallelogram = b × h

where,

  • b = base of the parallelogram
  • h = height of the parallelogram

Substituting the given values :-

⟶ 216 = 30 × h

⟶ 216/30 = h

⟶ 7.2 = h

Therefore, the height of the parallelogram = 7.2 cm

Similar questions