Ayush starts walking from his house to office.

Solution:

By given condition, we drawn a figure in which every place are indicated with his coordinates and direction also.

We know that,

distance between two points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$.

$d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

Now, distance between house and bank $=\sqrt{(5-2)^{2}+(8-4)^{2}}$

$=\sqrt{(3)^{2}+(4)^{2}}=\sqrt{9+16}=\sqrt{25}=5$

Distance between bank and daughter's school

$=\sqrt{(13-5)^{2}+(14-8)^{2}}=\sqrt{(8)^{2}+(6)^{2}}$

$=\sqrt{64+36}=\sqrt{100}=10$

Distance between daughter's school and office $=\sqrt{(13-13)^{2}+(26-14)^{2}}$

$=\sqrt{0+(12)^{2}}=12$

Total distance (House + Bank + School + Office) travelled = $5+10+12=27$ units

Distance between house to offices $=\sqrt{(13-2)^{2}+(26-4)^{2}}$

$=\sqrt{(11)^{2}+(22)^{2}}=\sqrt{121+484}$

$=\sqrt{605}=24.59 \approx 24.6 \mathrm{~km}$

So, extra distance travelled by Ayush in reaching his office = 27 – 24.6 = 2.4 km Hence, the required extra distance travelled by Ayush is 2.4 km.