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 touch at 70 cm above the garage floor. How wide is the garage?

Correct answer:

x =  4.7907 m

Step-by-step explanation:

$$\begin{gathered} a=2\text{m} \\ b=3\text{m} \\ c=0.70\text{m} \\ {x}_1=\sqrt{a^2-c^2}=\sqrt{2^2-0.7^2}\doteq 1.8735\text{m} \\ {x}_2=\sqrt{b^2-c^2}=\sqrt{3^2-0.7^2}\doteq 2.9172\text{m} \\ x=x_1+x_2=1.8735+2.9172=4.7907\text{m} \end{gathered}$$

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