SOLUTION: Find the value of x in the diagram: http://imgur.com/wCM3iVK Please show working out. Thanks

Algebra ->  Pythagorean-theorem -> SOLUTION: Find the value of x in the diagram: http://imgur.com/wCM3iVK Please show working out. Thanks      Log On


   

Question 1018487: Find the value of x in the diagram:
http://imgur.com/wCM3iVK
Please show working out. Thanks
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You can find the "altitude" of one of the slant triangles, and call this L. The slant triangle is an isosceles triangle.

%283%2F2%29%5E2%2BL%5E2=5%5E2
L%5E2=5%5E2-%283%2F2%29%5E2
L=sqrt%285%5E2-%283%2F2%29%5E2%29


The altitude of the pyramid is what you want next. A right triangle crossing through the pyramid altitude and a slant-altitude. Pythagorean Theorem formula again.
According to the figure,
x%5E2%2B%283%2F2%29%5E2=L%5E2
x%5E2=L%5E2-%283%2F2%29%5E2
highlight%28x=sqrt%28L%5E2-%283%2F2%29%5E2%29%29

You can substitute there for L^2 as found earlier, although was not simplified there;
highlight%28x=sqrt%285%5E2-%283%2F2%29%5E2-%283%2F2%29%5E2%29%29, and THIS you can now simplify and compute.