Question

What is the side of that equilateral triangle whose area costs as much to pave at Rs. 10 per square metre as it would cost to fence the three sides at Rs. 25 a metre?​

Answer 1

Question :-

What is the side of that equilateral triangle whose area costs as much to pave at Rs. 10 per square metre as it would cost to fence the three sides at Rs. 25 a metre?

Solution :-

Assume that the side of equilateral triangle is a metre

$\large \sf \: Area \: (A) = \frac{ { \sqrt{3} } }{4} \: {a}^{2} \: {m}^{2}$

$\implies\sf Cost \: of \: paving = 10 \:\times\frac{ \sqrt{3} }{4}\: {a}^{2} \: rupees$

$\large \sf \: Similarly, perimeter \: ( P) = 3a \: \: m$

$\large\implies\sf Cost \: of \: fencing \: =25 \times 3a \: rupees$

According to the equation.

$\large \sf \: 10 \times \frac{ \sqrt{3} }{4} \: {a}^{2} = 25 \times 3a$

$\large\implies \sf\: a = 10 \: \sqrt{3} m$

$\large \implies \: \sf \: a = 17.32 \: m$

Hence, the side of the equilateral triangle is 17.32 m.