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the square based pyramid has a base width of 2x cm. The vertical height of the pyramid is x cm. The length of all the slanted sides are 8¬3 (8 root 3). Find x.
can anyone help?
Very hard to explain without a picture. Here goes:
let the diagonal of the bas of the square be 2y.
this gives 2y2 (2 y squared) equals 2x all squared.
thus 2x2 (2 x squared) = y2 ( y squared)
Using the diagonal gives 8 root 3 all squared equals x squared plus y squared.
so y squared = 8 root 3 all squared - x squared.
so three x squared = 8 root 3 all squared.
solve this to give x = 8
gosh it is difficult! thank you, I think I get it :) x