Question

ABC is an isosceles triangle where AB =BC=12 cm and BC=8.Find the altitude on BC and hence calculate the area​

Answer 1

Answer:

8√2 cm is the altitude

32√2 is the

Step-by-step explanation:

Given triangle ABC and AB = AC = 12 cm

and BC = 8 cm

Let's draw a perpendicular from A to the base BC

also in an isosceles triangle, the perpendicular is the altitude of the isosceles triangle, I.e., AD bisects BC that is

BD = CD = 4cm

Now using pythagoras theorem,

AD² + BD² = AB²

Therefore, AD² = AB² - BD²

= 12² - 4²

= 144 - 16

= 128

Now, AD = √128

= 8√2 cm

ar(ABC) = (1/2)×base×altitude

= (1/2)×8×8√2

= 32√2 cm²