Question

can anybody solve ? example 10​

Answer 1

Answer:

Yes, as it is equilateral triangle.

Areas=

1. (1/2)×a^2
2. (1/2)×a^2
3. (1/2)×-(√3×a)^2

Answer 2

Answer:

Given=A(a,a),B(-a,-a),C(-√3a,√3a)

To prove=All sides are equal{AB=BC=CA)

d(AB)=√{(-a-a)^2+(-a-a)^2}

=√{(-2a)^2+(-2a)^2}

=√{(4a^2)+(4a^2)}

=√{8a^2 }

=2√2aunits ----(equation 1)

d(BC)=√{(-√3a+a)^2+(√3a+a)^2}

=√{a^2+3a^2-2√3a^2)+(3a^2+a^3+2√3a^2)}

=√{4a^2+4a^2}

=√(8a^2)

=2√2aunits -----(equation 2)

d(CA)=√{(a+√3a)^2+(a-√3a)^2}

=√{a^2+3a^2+2√3a^2+a^2+3a^2-2√3a^2}

=√{4a^2+4a^2}

=√(8a^2)

=2√2a^2units ----(equation 3)

from equation 1, 2 and 3

AB=BC=CA

Hence, It is an equilateral triangle

Side=2√2acm

Area of equilateral triangle=(√3)(a^2)/4

={(√3)(2√2cm)^2}/4

={(√3)(8cm^2)}/4

=2√3cm^2