Question

If each side of an equilateral triangle is doubled then what is the percentage increase in the area of the triangle

Answer 1

Area of equilateral triangle =root3/4×side square
let the side be x
let root 3/4 be y
area =yx^2
when sides are doubled
area=y(2x)^2=4yx^2
percentage increase = difference /initial area+×100
=4yx^2-yx^2/yx^2×100
=3/1×100=300 percent.

Answer 2

Step-by-step explanation:

Let, the equilateral triangle has sides of 'a' unit

Let, the equilateral triangle has sides of 'a' unitThen Area of the equilateral triangle =

Let, the equilateral triangle has sides of 'a' unitThen Area of the equilateral triangle =((√3)/4)*(a²) sq. unit

Let, the equilateral triangle has sides of 'a' unitThen Area of the equilateral triangle =((√3)/4)*(a²) sq. unitIf the sides of the triangle becomes '2a' unit

Let, the equilateral triangle has sides of 'a' unitThen Area of the equilateral triangle =((√3)/4)*(a²) sq. unitIf the sides of the triangle becomes '2a' unitNow the area of the equilateral triangle becomes =

Let, the equilateral triangle has sides of 'a' unitThen Area of the equilateral triangle =((√3)/4)*(a²) sq. unitIf the sides of the triangle becomes '2a' unitNow the area of the equilateral triangle becomes =((√3)/4)*(2a)² = ((√3)/4)*(4a²) sq. unit

Let, the equilateral triangle has sides of 'a' unitThen Area of the equilateral triangle =((√3)/4)*(a²) sq. unitIf the sides of the triangle becomes '2a' unitNow the area of the equilateral triangle becomes =((√3)/4)*(2a)² = ((√3)/4)*(4a²) sq. unitIncrease in area =

Let, the equilateral triangle has sides of 'a' unitThen Area of the equilateral triangle =((√3)/4)*(a²) sq. unitIf the sides of the triangle becomes '2a' unitNow the area of the equilateral triangle becomes =((√3)/4)*(2a)² = ((√3)/4)*(4a²) sq. unitIncrease in area ={ ((√3)/4)*(4a²) - ((√3)/4)*(a²) } sq. unit = 3a² sq. unit

Let, the equilateral triangle has sides of 'a' unitThen Area of the equilateral triangle =((√3)/4)*(a²) sq. unitIf the sides of the triangle becomes '2a' unitNow the area of the equilateral triangle becomes =((√3)/4)*(2a)² = ((√3)/4)*(4a²) sq. unitIncrease in area ={ ((√3)/4)*(4a²) - ((√3)/4)*(a²) } sq. unit = 3a² sq. unitPercentage Increase in area = ((3a²)/(a²))*100 = 300 %

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