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

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=
`(a*h)/(2)`

`h^(2) +((a)/(2))^(2)`=
`a^(2)`

`h^(2) = a^(2) - (a^(2) )/(4)`=
`(a^(2) )/(4)`*3

h=
`\sqrt{(a^(2)*3 )/(4) }`

h=
`(√(3)*a )/(2)`

replacing in the A equation:

A=
`(a*√(3)*a )/(2*2)`

A=
`(√(3)*a^(2) )/(4)`

Now each side increse by 50% ⇒ a=1.5a

A=
`(√(3)*(1.5a)^(2) )/(4)`

A=
`(√(3)*a^(2)* 2.25 )/(4)`

A=2.25 *
`(√(3)*a^(2) )/(4)`

It means that the area incrase by 225%