Question

Town $B$ is $13$ miles in the north and $84$ miles west of town $A$. How far are the two towns apart?

• A. $82$
• B. $81$
• C. $84$
• D. $85$

Answer 1

The correct option is D $85$

First draw the right-angled triangle $ABC$ showing that $B$ is $13$ miles north and 84 miles west of $A$:
In a right triangle, $a^2+b^2=h^2$, where $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse. This is called Pythagoras Theorem.
$BC=13,CA=84,AB=$ hypotenuse side $=?$
${13}^2+{84}^2=A{B}^2$
$169+7056=$ $A{B}^2$
$A{B}^2$ $=7225$
Taking root on both the sides, we get
$AB=85$