# Laths

There are two laths in the garage opposite one another: one 2 meters long and the other 3 meters long. They fall against each other and lean against the opposite walls of the garage both laths and touch at a height of 70 cm above the garage floor. How wide is the garage?

Result

x =  4.791 m

#### Solution:

$a=2 \ \text{m} \ \\ b=3 \ \text{m} \ \\ c=0.70 \ \text{m} \ \\ x_{1}=\sqrt{ a^2- c^2 }=\sqrt{ 2^2- 0.7^2 } \doteq 1.8735 \ \text{m} \ \\ x_{2}=\sqrt{ b^2- c^2 }=\sqrt{ 3^2- 0.7^2 } \doteq 2.9172 \ \text{m} \ \\ x=x_{1}+x_{2}=1.8735+2.9172 \doteq 4.7907 \doteq 4.791 \ \text{m}$

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