:Corresponding base of the bigger triangle (i.e, the triangle with area A₁), b₂ = 6 cmExplanation :Given :Ratio of the areas of the two triangle, A₁ : A₂ = 2 : 3Base of the smaller triangle (i.e, the triangle with area A₁), b₁ = 4 cmHeight of the triangle are equal.To find :Corresponding base of the bigger triangle (i.e, the triangle with area A₁), b₂ = ?KNOWLEDGE required :Formula for Area of a triangle :⠀⠀⠀⠀⠀⠀⠀⠀⠀A = ½ × b × h⠀[Where : A,b and h are the area, base and height of the triangle, respectively]Solution :LET the height of the two TRIANGLES be h cm (Since, they are equal).[The ratio of the areas of the triangle will be equal to the ratio of the area of the triangle (in form of formula)]Now, by using the formula for area of a triangle, we get :⠀⠀⠀=> A₁/A₂ = (½ × b₁ × h)/(½ × b₂ × h)⠀⠀⠀=> ⅔ = (½ × 4 × h)/(½ × b₂ × h)⠀⠀⠀=> ⅔ = 4/b₂⠀⠀⠀=> 2 × b₂ = 4 × 3⠀⠀⠀=> 2b₂ = 12⠀⠀⠀=> b₂ = 12/2⠀⠀⠀=> b₂ = 6⠀⠀⠀⠀⠀⠀∴ b₂ = 6 cmHence, the corresponding base of the bigger triangle (i.e, the triangle with area A₁) is 6 cm.