Question

Going 45m toward south of her house, Ankita turns left and goes another 20m. She turns north and goes 30m and
then starts walking toward her house. How far is she from the starting point and in which direction is she walking
now?​

Answer 1

Answer :

25 metres

Explanation :

Let's say the house is at point A,

Walking 45m towards South and reaches point B after that turning left and walks 20m.

And then, 30m towards her house (north).

Now,

Let's say that Ankita is $x$m away from the starting point.

[following the figure]

In ∆ABE,

BE(perpendicular) = 20m.

And we can say that,

AE(base) will be : AD - BC

= 45 - 30

= 15m

Now, in the ∆ABE we have,

• AE(base) = 15m.
• BE(perpendicular) = 20m.

By Pythagoras theorem :

$\implies \: {x}^{2} = { {(15)}^{2} + {(20)}^{2} }$

Solving for $\boldsymbol{x}$

$\implies \: {x}^{2} = {15}^{2} + {20}^{2}$

$\implies \: {x}^{2} = {225 + 400}$

$\implies \: {x}^{2} = 625$

$\implies \: {x} = \sqrt{625}$

$\implies \: x = 25$

Therefore, Ankita is 25m away from his starting point.