A15-meter by 23-meter garden is divided into two sections. two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section.

what is the approximate sum of the lengths of the two sidewalks, shown as dotted lines?

a. 21.2 m
b. 27.5 m
c. 32.5 m
d. 38.2 m

Solution:

We have re-drawn the given diagram, as we can see the given rectangle is actually divided into two parts.

one is Large square and the other one is a smaller rectangle.

Now we will apply the Pythagoras theorem in the larger triangle which is inside the square.

So we can write

Now we will apply the Pythagoras theorem in the smaller  triangle which is inside the smaller rectangle.

So we can write

The approximate sum of the lengths of the two sidewalks, shown as dotted lines m

Hence the correct option is D