Question

In this figure $\angle ABC = 90^\circ$ and $BD \bot AC$. If AB=5.7 cm, BD=3.8 cm and CD=5.4 cm, find BC.

Answer 1

Hint: Here, we will apply the concepts of geometry and Pythagoras theorem to find the value of the side BC.

Complete step-by-step answer:
Here in this question we don’t have to look at any other thing except triangle BDC.
We know the value of BD and CD as well.
We have to find the length of side BC.
We also know triangle BDC is right angled at D. As BD is perpendicular on AC.
Then we can simply apply Pythagoras formula on triangle BDC and get BC.
So, we get,
$
  B{C^2} = B{D^2} + C{D^2} \\
  B{C^2} = {3.8^2} + {5.4^2} \\
  BC = \sqrt {14.44 + 29.16} = 6.60{\text{ cm}} \\
 $
Hence $BC = 6.60{\text{ cm}}$

Note: Whenever this type of problem arises observe the geometry carefully and think that one can do & also be careful about data which is of no use in your solution then apply the basics of geometry and get the answers.