# In the DeltaABC below, M and N are midpoints of BC and AB respectively, m/_A=90^@. Find x,y and z?

Jul 6, 2016

$x = 9.67$, $y = 2$ and $z = 36$

#### Explanation:

As M is the midpoint of BC, we have

$36 = 40 - 2 y$ and transposing similar terms we get

$2 y = 40 - 36 = 4$. Hence, $y = 2$.

As $M$ is the midpoint of $B C$ and it joins mid point of $A B$ at the base at $N$, then $M N$ is half of $A C = 36$ and hence

$3 x - 11 = \frac{36}{2} = 18$ i.e.

$3 x = 18 + 11 = 29$ and $x = \frac{29}{3} = 9.67$.

As $M N$ joins mid points of $A B$ and $B C$, it too is perpendicular to $A B$ (as $M N$||$A C$) and $\Delta s M N B$ and $A M N$ are congruent (SAS) and hence $B M = A M$.

Hence, $z = 36$.