Question

side of an equilateral triangle is 8cm find the side of an equilateral triangle where area is twice the area of first​

Answer 1

Given :-

Side of equilateral triangle = 8 cm

We know that all sides of equilateral triangle are equals !

We have to find the Side of triangle whose area is twice the area of 1st

$\boxed{\sf\ \ Area\ of \ equilateral\ \triangle= \dfrac{\sqrt{3}}{4}a^2}$

Where a = side

$\longrightarrow\sf Area = \dfrac{\sqrt{3}}{4}\times (8)^2\\ \\ \longrightarrow\sf Area = \dfrac{\sqrt{3}}{\cancel{4}}\times \cancel{64}\\ \\ \longrightarrow\sf Area = \sqrt{3}\times 16\\ \\ \longrightarrow\sf Area \ of \ equilateral \triangle = 16\sqrt{3}cm^2$

Now the Area of that triangle whose area is twice the first

$\longrightarrow\sf Area \ of \ \triangle_2= 2\times 16\sqrt{3}\\ \\ \longrightarrow\sf Area \ of \ \triangle_2= 32\sqrt{3}cm^2$

Now the side of triangle 2

$\longrightarrow\sf \dfrac{\sqrt{3}}{4}a^2= 32\sqrt{3}\\ \\ \longrightarrow\sf a^2= 32\cancel{\sqrt{3}}\times \dfrac{4}{\cancel{\sqrt{3}}}\\ \\ \longrightarrow\sf a^2= 128\\ \\ \longrightarrow\sf a= \sqrt{2\times 4\times 4\times 4}\\ \\ \longrightarrow\sf a= 8\sqrt{2}cm$

$\boxed{\sf \dag\ \ Side\ of \ triangle_2= 8\sqrt{2}cm}$

Answer 2

GIVEN:

• Side of equilateral triangle ( ∆₁ ) = 8cm
• Area of other equilateral triangle ( ∆₂ ) = Twice of equilateral triangle ( ∆₁ )

TO FIND:

• Side of other equilateral triangle ( ∆₂ ) = ?

SOLUTION:

Let

• Equilateral triangle be : ‘∆₁’
• Other Equilateral triangle be : ‘∆₂’

We know that

Area of equilateral triangle = √3/4 × (side)²

∆₁ = √3/4 × 8²

∆₁ = 16√3 cm²

Given, area of other equilateral triangle = 2( Area of equilateral triangle . Writing in the form of equation

∆₂ = 2 ( ∆₁ )

→ √3/4 (side)² = 2( 16√3 )

→ side² = 32√3 × 4/√3

→ side = √128

→ Side = 8√2 cm

Hence, side of othe equilateral triangle ( ∆₂ ) = 8√2 cm