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. 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

Explanation:

Step1: Calculate the diagonal of the square section

The square section has side length \(a = 15\)m. Using the Pythagorean theorem for a square's diagonal \(d_1=\sqrt{15^{2}+15^{2}}=\sqrt{2\times15^{2}} = 15\sqrt{2}\approx15\times1.414 = 21.21\)m.

Step2: Calculate the diagonal of the smaller rectangular section

The smaller rectangular section has length \(l=23 - 15=8\)m and width \(w = 15\)m. Using the Pythagorean theorem \(d_2=\sqrt{8^{2}+15^{2}}=\sqrt{64 + 225}=\sqrt{289}=17\)m.

Step3: Calculate the sum of the two diagonals

\(S=d_1 + d_2\approx21.21+17=38.21\)m.

Answer:

38.2 m