Question

applying the pythagorean theorem
#1. layne rode his bike from point a to b by using cherry street. how much further would his trip have been if he took orange drive and peach avenue instead?
a
orange dr.
cherry st.
85 yd
77 yd
b
peach ave.

Explanation:

Step1: Find length of Orange Dr. using Pythagorean theorem

Let the length of Orange Dr. be $x$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 85$ (Cherry St.) and $b=77$ (Peach Ave.). So $x=\sqrt{85^{2}-77^{2}}=\sqrt{(85 + 77)(85 - 77)}=\sqrt{162\times8}=\sqrt{1296}=36$ yards.

Step2: Calculate total distance of Orange Dr. and Peach Ave.

The total distance of taking Orange Dr. and Peach Ave. is $36 + 77=113$ yards.

Step3: Find the difference in distances

The distance of taking Cherry St. is 85 yards. The difference is $113-85 = 28$ yards.

Answer:

28