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# From scnool, you biked 1.2 miles due south and then 0.5 mile due east to your house. If you had biked home on the street that runs directly diagonal from your school to your house, how many fewer miles would you have biked?

Equations and inequalities
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asked 2021-03-08
From scnool, you biked 1.2 miles due south and then 0.5 mile due east to your house. If you had biked home on the street that runs directly diagonal from your school to your house, how many fewer miles would you have biked?

## Answers (2)

2021-03-09
The actual distance you biked is 1.2+0.5=1.7 miles.
The length of the diagonal, x, is the hypotenuse of the right triangle formed by the 2 given distances as the legs. By Pythagorean Theorem, $$\displaystyle{1.2}^{{2}}+{0.5}^{{2}}={x}^{{2}}$$
$$\displaystyle{1.44}+{0.25}={x}^{{2}}$$
$$\displaystyle{1.69}={x}^{{2}}$$
$$\displaystyle√{1.69}={x}$$
x=1.3 miles
So, you would have bikes 1.7−1.3=0.4 miles fewer.
2021-08-10

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