Question

ABC is an isoceles triangle with AB=AC=12cm and BC=8cm. Find the altitude on BC and hence calculate its area.

Answer 1

Let D be the mid point of BC.
Thus, BD =CD = 4cm

Join AD
AB² = AD² + CD² or
AD² = AB² - CD²
AD = √((12cm)² - (4cm)²)
AD = √(144 cm² - 16cm²)
AD = √128cm²
AD = √( (2 × 2) × (2 ×2) ×(2 ×2) × 2 ×1cm x 1cm)
AD = 2 × 2 × 2 × √2 × 1cm
AD = 8√2cm

Area of triangle ABC = (1/2) × BC × AD
= (1/2) × 8 cm × 8√2 cm
= 4 cm × 8√2 cm
= 32√2 cm². ANS

Answer 2

construct an altitude on BC
then using hypotenuse theorem
12^2 - (8/2)^2 = Altitude^2
= 144 - 16
Altitude = √128

area= 1/2 × base × height
= 1/2 × 12 × √128
Area =6√128