Question

calculate the area of triangle whose sides are 18cm,24cm,and 30cm in length .Find the length of altitude corresponding to smallest side.​

Answer 1

Answer:   The ‘area of triangle’ is 216 and ‘Altitude’ = 24 cm  

Step-by-step explanation:  

To find:

• ‘Area of triangle’ & ‘length of the altitude’ corresponding to the ‘smallest side’.

• Solution: ..........................

•       Given: Sides are 18 cm, 24 cm and 30 cm in length.  

• Firstly, we need to find s i.e., half of the triangles perimeter    whereas a, b & c are three sides of triangle.

• Secondly, the formula for ‘area of triangle’ is

• Thirdly, shortest side = 18 cm

• Area of triangle = 216

• Hence, Altitude = 24 cm i.e. corresponding to shortest side

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Answer 2

Find the semi-perimeter:  

p = (18 + 24 + 30) ÷ 2 = 36 cm

Find the area of the triangle:

area = √p(p-a)(p-b)(p-c)  

area = √36(36 - 18)(36 - 24)(26 - 30)  

area = √46656  

area = 216 cm²  

Find the length of the altitude corresponding to the smallest side:

area = 1/2 (base) (height)

216 = 1/2 (18) (height)  

216 = 9 height  

height = 216 ÷ 9 = 24 cm

Answer: The area is 216 cm² and the corresponding height is 24 cm

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