a 15 - meter by 23 - meter garden is divided into two sections. two sidewalks run along the diagonal of the…

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. 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

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. 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

Explanation:

Step1: Calculate diagonal of square

The square has side - length 15 m. Using the Pythagorean theorem (d_1=\sqrt{15^{2}+15^{2}}) for a right - triangle with sides (a = b=15) m. [d_1=\sqrt{2\times15^{2}} = 15\sqrt{2}\approx15\times1.414 = 21.21]

Step2: Calculate diagonal of rectangle

The rectangle has sides 15 m and (23 - 15=8) m. Using the Pythagorean theorem (d_2=\sqrt{15^{2}+8^{2}}). [d_2=\sqrt{225 + 64}=\sqrt{289}=17]

Step3: Calculate sum of diagonals

Find the sum (S=d_1 + d_2). [S\approx21.21+17=38.21\approx38.2]

Answer:

38.2 m