Question

Find the length of dm in the given fig.​

Answer 1

Answer:

$DM=12$

Step-by-step explanation:

(Let the point where the altitude from $D$ intersects $AB$ be called as point $E$.) First, let's find the area of parallelogram $ABCD$. The area of a parallelogram is simply $b*h=bh$, where $b$ is the parallelogram's base and $h$ is the parallelogram's height. If we let $AB$ and $DE$ be the base and height respectively, since we are already given their lengths, we know that the area of parallelogram $ABCD$ will be $AB*DE=15*8=120$.

Now, how does this information matter, you might ask? Well, we can take either $AB$ or $CB$ to be the base and either $DE$ or $DM$ to be the height. In this case, let's take the latter two options, as we are looking to find the length of $DM$.

Therefore, we know that the area of parallelogram $ABCD$ can also be found by calculating $CB*DM$. Since we know the values of the area and $CB$, we can write the following equation to solve for $DM$:

$Area = CB*DM$

$120=10*DM$ (Substitute $Area=120$ and $CB=10$ into the equation)

$\frac{120}{10}=\frac{10*DM}{10}$ (Divide both sides of the equation by $10$ to get rid of $DM$'s coefficient)

$12=DM$ (Simplify)

$DM=12$ (Symmetric Property of Equality)

Hope this helps!