The diagram shows a right angled triangle with two other smaller right angled triangles inscribed in it.
The bigger of the two inscribed triangles is to the left with sides 9 and h.
The smaller of the two inscribed triangles is to the right with sides 4 and h.
Observe carefully, that the left triangle has
Shorter side = h
Longer side = 9
Similarly, the triangle on the right has
Shorter side = 4
Longer side = h.
Therefore we can use the ratio,
[tex]\begin{gathered} \frac{\text{shorter side}}{longer\text{ side}}=\frac{shorter\text{ side}}{longer\text{ side}} \\ \frac{h}{9}=\frac{4}{h} \\ \text{Cross multiply and you now have;} \\ h^2=36 \\ h=\sqrt[]{36} \\ h=6 \end{gathered}[/tex]
The altitude h, equals 6
The correct answer is option D, that is 6 units
