Question

This figure illustrates the measures of a parking lot in meters. What is the length in centimeters of line segment BD?

Answer 1

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:

`AE=21-15=6m`

Now, we have a right triangle:

We can find the length of EC using the pythagorean theorem:

`AC^2=AE^2+EC^2`

Then, we can substitute with the known values:

`10^2=6^2+EC^2`

And solve for EC:

`\begin{gathered} 100=36+EC^2 \\ . \\ 100-36=EC^2 \\ . \\ EC=√(64) \\ . \\ EC=8m \end{gathered}`

Thus:

`BD=8m`

But, we need to write the answer in cm. Since there are 100 cm in a meter:

`8\cdot100cm=800cm`The answer is:
`BD=800\text{ }cm`