# CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.5 Question 11

CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.5 Question 11

11 .    An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after $1\frac{1}{2}$ hours?

Solution:

Distance traveled by aeroplane in $1\frac{1}{2}$ hrs towards North direction = $1000 \times \frac{3}{2}$ = 1500 km

Distance traveled by other aeroplane in $1\frac{1}{2}$ hrs towards West direction = $1200 \times \frac{3}{2}$ = 1800 km

We want to find distance (AC) between two aeroplanes after $1\frac{1}{2}$ hrs

Using Pythagoras theorem, we get

$AC^2 = AB^2 + BC^2$

$\Rightarrow AC^2 = (1500)^2 + (1800)^2 = 2250000 + 3240000 = 5490000$

$\Rightarrow AC = \sqrt{5490000} = 300\sqrt{61}$ Km

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