Question

Rupa goes for a walk every morning in the park close to her apartment. The park is in the shape of a rectangle of length 40 m and width 30 m, as shown in the figure below. She walks around the park 5 times daily. Due to some construction work she cannot go along her normal path tomorrow, she will have to take the route from one corner of the park (A) to the diagonally opposite corner (C).

How many times will she have to walk on the new path (A-C) tomorrow, to cover the same distance as she used to cover each day earlier?

• A. 5 times
• B. 1 time
• C. 14 times
• D. 16 times

Answer 1

The correct option is C

14 times

We know that, in triangle ADC, $\angle D$ = ${90}^{\circ }$​
Therefore, using Pythagoras Theorem, we get:
$A{C}^2=A{D}^2+D{C}^2={\left(40m\right)}^2+{\left(30m\right)}^2=1600m^2+900m^2=2500m^{2}AC=\sqrt{2500}{m}^2=50m$
Her old path was ABCD, which is equal to (30 + 40 + 30 + 40) m = 140 m.
She used to run 5 times a day. So, Total Distance = $5\times 140$ m = 700 m.
So, let x be the number of times she will have to walk on path A-C tomorrow. Since the distance has to be the same, therefore
$x\times AC$= 700 m
$x\times 50m$ = 700 m
$x=\frac{700m}{50m}=14$ times.