Answer:
x = 4
Step-by-step explanation:
Right Triangles
In right triangles, where one of the internal angles is 90°, the Pythagora's Theorem is satisfied:
If m is the hypotenuse of a right triangle, and p, q are the shorter sides or legs, then:
[tex]m^2=p^2+q^2[/tex]
If we need to calculate any of the legs, say, p:
[tex]p^2=m^2-q^2[/tex]
The figure below shows two additional variables z and h which will help us to find the value of x.
The triangle with sides 12, 36, z can be solved for z, being 36 the hypotenuse:
[tex]z^2=36^2-12^2=1296-144=1152[/tex]
The base of the triangle to the left is (36-x), the height is h, and the hypotenuse is z, thus:
[tex]h^2=z^2-(36-x)^2[/tex]
Substituting z:
[tex]h^2=1152-(36-x)^2[/tex]
The triangle to the right has dimensions x, h, and 12, and:
[tex]h^2=12^2-x^2[/tex]
Equating both expressions for h:
[tex]1152-(36-x)^2=12^2-x^2[/tex]
Expanding the squares:
[tex]1152-1296+72x-x^2=144-x^2[/tex]
Simplifying the x squared and operating:
-144+72x=144
Adding 144:
72x = 288
Solving:
x = 288 / 72 =4
x = 4
