Question

if the side of an equilateral triangle is r, then the area of the triangle varies directly as

Answer 1

Area of equilateral triangle = root 3a / 4

Therefore area is directly varying with side

Hope it helps u

@skb

Answer 2

If the side of an equilateral triangle is r, then the area of the triangle varies directly as r²

Given : The side of an equilateral triangle is r

To find : The area of the triangle varies directly as

Solution :

Step 1 of 2 :

Find the area of the triangle

The side of an equilateral triangle is r

Let A be the area of the triangle

Then we have

$\displaystyle \sf{A = \frac{ \sqrt{3} }{4} {r}^{2} }$

Step 2 of 2 :

Find the result

$\displaystyle \sf{A = \frac{ \sqrt{3} }{4} {r}^{2} }$

$\displaystyle \sf{ \implies \: A = k{r}^{2} } \: \: where \: k = \frac{ \sqrt{3} }{4}$

$\displaystyle \sf{ \implies \: A \propto{r}^{2} }$

Thus we have area of the triangle varies directly as r²

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