Question

A 15-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.

A rectangle is shown. The length of the top and bottom sides is 23 meters. The length of the left and right sides is 15 meters. A vertical line is drawn from the top to bottom side to split the shape into a square and a rectangle. Lines are drawn from the bottom left point to the top of the vertical line and from the bottom right point to the top of the vertical line.

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

21.2 m
27.5 m
32.5 m
38.2 m

Answer 1

Answer: the answer is D. 38.2 m.

Step-by-step explanation: it is show below.

Answer 2

Option D) 38.2

Solution

1) The square section

The side length of the square is 15m.

You can use Pythagoras's theorem to find the length of the diagonal:

Diagonal ^2 = (15m)^2 + (15m^2) = 450 m^2

=> Diagonal = √(450m^2) = 21.21m

2) The small rectangle section

The sides of this rectangle are 23 - 15 = 8 m and 15 m

Now use the Pythagoras's theorem:

diagonal^2 = (8m)^2 + (15m)^2 = 289 m^2 =>

diagonal = √(289m^2) = 17 m

3) Then the sum of the lengths of the diagonals of the two sections is 17m + 21.21 m = 38.21

Answer: 38.21 m