Question

The altitude of an equilateral triangle is 2√3, The ratio of its perimeter to area is
i) 1:√3
ii)√3:1
iii)1:3
iv)3:1​

Answer 1

Step-by-step explanation:

let a be side of equilateral triangle

altitude of equilateral triangle will bisect the base

Answer 2

Answer:

the answer is option ii)

$\sqrt{3} :1$

Step-by-step explanation:

altitude of equilateral traingle is given as

$2 \sqrt{3}$

now we know the formula of altitude of equilateral triangle as

$altitude \: of \: equilateral \: triangle \: = \frac{1}{2} \times \sqrt{3} \times side \\ </p><p>$

Now calculating the side from the above formula,

$altitude \: of \: equilateral \: triangle \: = \frac{1}{2} \times \sqrt{3} \times side \\ </p><p>2 \sqrt{3} = \frac{1}{2} \times \sqrt{3 } \times side \\ \frac{2 \sqrt{3} }{ \sqrt{3} } \times 2 = side \\ 4 \: units = side$

side = 4 units

Now by the formula of

area of equilateral triangle,

$area \: of \: equilateral \: triangle = \frac{1}{4} \times \sqrt{3} \times {side}^{2} \\ = \frac{1}{4} \times \sqrt{3} \times {4}^{2} \\ = 4 \sqrt{3} sq \: units$

Now we will find the perimeter of equilateral triangle

$perimeter \: of \: equilateral \: triangle = 3 \times side \\ = 3 \times 4 \\ = 12units$

Ratio Of perimeter to area is,

$\frac{perimeter}{area} = \frac{12}{4 \sqrt{3} } \\ = \frac{3}{ \sqrt{3} } \\ = \frac{ \sqrt{3} \sqrt{3} }{ \sqrt{3} } \\ = \sqrt{3} \\ perimeter:area \: = \sqrt{3}:1$

ignore <p>