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=[tex]\frac{a*h}{2}[/tex]
[tex]h^{2} +(\frac{a}{2})^{2}[/tex]=[tex]a^{2}[/tex]
[tex]h^{2} = a^{2} - \frac{a^{2} }{4}[/tex]= [tex]\frac{a^{2} }{4}[/tex]*3
h=[tex]\sqrt{\frac{a^{2}*3 }{4} }[/tex]
h=[tex]\frac{\sqrt{3}*a }{2}[/tex]
replacing in the A equation:
A=[tex]\frac{a*\sqrt{3}*a }{2*2}[/tex]
A=[tex]\frac{\sqrt{3}*a^{2} }{4}[/tex]
Now each side increse by 50% ⇒ a=1.5a
A= [tex]\frac{\sqrt{3}*(1.5a)^{2} }{4}[/tex]
A=[tex]\frac{\sqrt{3}*a^{2}* 2.25 }{4}[/tex]
A=2.25 * [tex]\frac{\sqrt{3}*a^{2} }{4}[/tex]
It means that the area incrase by 225%
