Question

If the length of each side of an equilateral triangle were increased by 50 percent, what would be the percent increase in the area?

Answer 1

Answer:

The area increase by 225%

Step-by-step explanation:

attachment of a triangle

The area of a triangle equilateral is calculated with the next formula:

A=$\frac{a*h}{2}$

$h^{2} +(\frac{a}{2})^{2}$=$a^{2}$

$h^{2} = a^{2} - \frac{a^{2} }{4}$= $\frac{a^{2} }{4}$*3

h=$\sqrt{\frac{a^{2}*3 }{4} }$

h=$\frac{\sqrt{3}*a }{2}$

replacing in the A equation:

A=$\frac{a*\sqrt{3}*a }{2*2}$

A=$\frac{\sqrt{3}*a^{2} }{4}$

Now each side increse by 50% ⇒ a=1.5a

A= $\frac{\sqrt{3}*(1.5a)^{2} }{4}$

A=$\frac{\sqrt{3}*a^{2}* 2.25 }{4}$

A=2.25 * $\frac{\sqrt{3}*a^{2} }{4}$

It means that the area incrase by 225%