Question

The cost of painting a signboard shaped like an equilateral triangle is 4356 dollars. If the cost of painting another signboard with area 31 cm2 is 1023 dollars, what is the side of the equilateral triangle?

Answer 1

The cost of painting a sign board of area 31 cm² is $1023

So the cost of painting per square cm is

$\frac{1023}{31}= 33$

The cost of painting per square cm is $33

The cost of painting the triangular sign board is $4356

Hence the area of the triangular sign board is

= $\frac{4356}{33} =132$

Now the area of the triangular sign board is 132 cm²

But the triangle is an equilateral triangle

The area of equilateral triangle is

$\frac{\sqrt{3}}{4}s^{2}$

so$\frac{\sqrt{3}}{4}s^{2}=132$

Multiplying by

$\frac{4}{\sqrt{3}}$

on both sides

we get

$s^{2}=\frac{132(4)}{\sqrt{3}}$

Taking square root on both sides we get

$s=\sqrt{ \frac{132(4)}{\sqrt{3}} }=17.5cm$

Hence the side of the triangle is 17.5 cm