Question

#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. 48 yards

Explanation:

Step1: Use Pythagorean theorem to find length of Orange Dr.

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 $x=\sqrt{85^{2}-77^{2}}$.
\[

$$\begin{align*} x&=\sqrt{(85 + 77)(85 - 77)}\\ &=\sqrt{162\times8}\\ &=\sqrt{1296}\\ & = 36 \end{align*}$$

\]

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

The sum of the lengths of Orange Dr. and Peach Ave. is $36+77 = 113$ yards.

Step3: Find the difference in distances.

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

Answer:

28