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Pranali and Prasad Started Walking to the East and to the North Respectively, from the Same Point and at the Same Speed. After 2 Hours Distance Between Them Was 15 √ 2 Km. Find Their Speed per Hour. - Geometry

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Question

Pranali and Prasad started walking to the East and to the North respectively, from the same point and at the same speed. After 2 hours distance between them was \[15\sqrt{2}\]

 km. Find their speed per hour.

 

Solution

It is given that, Pranali and Prasad have same speed.
Thus, they cover same distance in 2 hours.
i.e. OA = OB

Let the speed be x km per hour.

According to Pythagoras theorem,
In ∆AOB

\[{AB}^2 = {AO}^2 + {OB}^2 \]
\[ \Rightarrow \left( 15\sqrt{2} \right)^2 = {AO}^2 + {OA}^2 \]
\[ \Rightarrow 450 = 2 {AO}^2 \]
\[ \Rightarrow {AO}^2 = \frac{450}{2}\]
\[ \Rightarrow {AO}^2 = 225\]
\[ \Rightarrow AO = 15 km\]
\[ \Rightarrow BO = 15 km\]

\[\text{Speed} = \frac{Distance}{Time}\]
\[ = \frac{15}{2}\]
\[ = 7 . 5 \text{km per hour}\]

  Is there an error in this question or solution?

APPEARS IN

 Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 2: Pythagoras Theorem
Problem Set 2 | Q: 10 | Page no. 45
Solution Pranali and Prasad Started Walking to the East and to the North Respectively, from the Same Point and at the Same Speed. After 2 Hours Distance Between Them Was 15 √ 2 Km. Find Their Speed per Hour. Concept: Pythagoras Theorem.
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