Question

a right angled isosceles triangle has hypotenuse of 12 cm .its area

Answer 1

let ABC be a right angled isosceles triangle whose hypotenuse is 12cm(AC)
by Pythagoras theorem
AC²=AB²+BC²
AB=BC(ABC is an isosceles triangle)
AB²=BC²
AC²=AB²+BC²
AC²=AB²+AB²
(12cm)²=2AB²
144cm²=2AB²
AB²=144cm²/2
AB²=72cm²
AB=√72cm²
AB=6√2 cm
therefore BC=6√2cm
area of triangle=1/2×AB×BC
=1/2×6√2cm×6√2cm
=1/2×72cm²
=36 cm²

Therefore,the area of triangle is 36cm²

Answer 2

AC2 = AB2 + BC2

12*12 = 2(AB)2

144/2 = AB2

√72 =AB

AB = 6√2

1/2 × b × h

1/2 × 6√2 *6√2

36 cm2