Question

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The area of equilateral triangle is 16√3 cm². Find its area and also the length of the smallest altitude.

Answer 1

Given, area of an equilateral triangle = 16√3 cm^2

Area of an equilateral triangle = √3/4 (side)^2

√3/4(Side)^2 = 16√3 ⇒  (Side)^2 = 64

⇒ Side =8 cm

[taking positive square root because side is always positive]

Perimeter of an equilateral triangle = 3 x Side= 3 x 8 = 24 cm

Hence, the perimeter of an equilateral triangle is 24 cm.

Area of triangle= 1/2 × base× hight

16√3 cm².=1/2×8 × hight

16√3 cm² ×2÷8.= high =4 cm

the length of the smallest altitude= 4 cm ANS

Answer 2

Given that

Area of equilateral triangle = 16√3 cm²

We have to find its side and the length of smallest altitude.


=> All the altitude would be of same length as it is an equilateral triangle. So, we just have to find the altitude.


Area of an equilateral triangle is given as √3/4 a²

where, a² = square of side.

=> √3/4 × a² = 16√3

=> a² = 16√3 × 4/√3

=> a² = 16 × 4

=> a² = 64

=> a = √64 = 8 cm

Hence, the side of the ∆ is 8cm.

Now, we have to find the altitude.

Area of a ∆ is also given by

1/2 × base × altitude

=> 1/2 × 8 × altitude = 16√3

=> 4 × altitude = 16√3

=> altitude = 16√3 ÷ 4

=> altitude = 4√3 cm


Hence, the altitude is 4√3 cm

Hope it helps dear friend ☺️✌️✌️