Question

A boat travels $10$ miles East and then $24$ miles South to an island. How many miles are there from the point of departure of the boat to the island?

• A. $34$
• B. $14$
• C. $26$
• D. $2\sqrt{119}$
• E. $44$

Answer 1

Answer: (C)

$26$

While travelling to $10$ miles East and then $24$ miles South the boat is moving on the path to form a right angled triangle.
The distance $c$ then would be the hypotenuses of the triangle, which can be calculated using Pythagorean Theorem which is $a^2{+b}^2=c^2$.
As we have the measurements of the two sides making the right angle:
$\Rightarrow {10}^2{+24}^2=c^2$
$\Rightarrow 100+576=$ $c^2$
$\Rightarrow c^2$ $=676$
$\Rightarrow c$ $=26$ miles
Hence, the option C is the right answer.
Ans: C