The diagram of the parking lot is:
We can draw a line to divide the figure into a rectangle and a right triangle:
And we can see that:
BD = EC
AE = AB - CD
And since we know:
AB = 21m
CD = 15m
We can find the length of AE:
[tex]AE=21-15=6m[/tex]
Now, we have a right triangle:
We can find the length of EC using the pythagorean theorem:
[tex]AC^2=AE^2+EC^2[/tex]
Then, we can substitute with the known values:
[tex]10^2=6^2+EC^2[/tex]
And solve for EC:
[tex]\begin{gathered} 100=36+EC^2 \\ . \\ 100-36=EC^2 \\ . \\ EC=\sqrt{64} \\ . \\ EC=8m \end{gathered}[/tex]
Thus:
[tex]BD=8m[/tex]
But, we need to write the answer in cm. Since there are 100 cm in a meter:
[tex]8\cdot100cm=800cm[/tex]
The answer is:[tex]BD=800\text{ }cm[/tex]
