Question

1. most days, marcus drives from his home to his office along the solid line segments shown. some days, he takes a shortcut and rides his bike along the dashed line segment. how much farther does marcus travel when he drives than when he rides his bike?

home
office
a. 1 mile
c. 3 miles
b. 2 miles
d. 5 miles
a rectangular rug is 12 feet long and has a diagonal measure of 15 feet. determine the area, enter your

Explanation:

Step1: Calculate driving distance

Marcus drives along two sides of a right - triangle. The lengths of the two sides are \(3\) miles and \(4\) miles. So the driving distance \(d_{drive}=3 + 4\).

$$d_{drive}=7$$

Step2: Calculate biking distance

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 3\), \(b = 4\). Then \(c=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}\).

$$c = 5$$

Step3: Calculate the difference

The difference in distance \(\Delta d=d_{drive}-d_{bike}\). Substitute \(d_{drive}=7\) and \(d_{bike}=5\) into the formula.

$$\Delta d=7-5$$

$$=2$$

Answer:

B. 2 miles