Answer:
Step-by-step explanation:
In the first triangle, you have the following relation between a, b and h.
[tex]\frac{a}{h} = \frac{h}{b}[/tex]
This is another form of the Altitude Theorem in a right triangle.
In the second example, we use the Altitude Theorem:
Let h denote the dotted line / the altitude;
[tex]h^2 = 7 \cdot 9 = 36[/tex]
h = 6, we take the positive version since we're in Euclidean Geometry.
Now we have to solve for x. It's easy since the h that we solved for is in a right triangle and we have Pythagora's Theorem for that.
It states: [tex]x^2 = 6^2 + 9^2 = 117 [/tex]
So [tex]x = \sqrt{117}[/tex]
