Solved
This can be solved using simultaneous equations. Please refer to the diagram for the labelling.
From the diagram we can see (by Pythagoras' Theorem):
$\displaystyle a^2+b^2 = 7^2$ ...[1]
$\displaystyle b^2 + c^2 = 35^2$ ...[2]
$\displaystyle c^2+d^2 = 49^2$ ...[3]
$\displaystyle a^2+d^2 = x^2$ ...[4]
Subtracting the first from the second,
$\displaystyle c^2 - a^2 = 35^2 - 7^2$
$\displaystyle c^2 - a^2 = 1176$ ...[5]
Then, subtracting [5] from [3],
$\displaystyle a^2 + d^2 = 49^2 - 1176$
So we have $\displaystyle x^2 = 49^2 - 1176=1225$
$\displaystyle x = 35$
I don't get why $\displaystyle a^2 + b^2 = 7^2$. If this is the Pythagorean theorem, how did you come to that equation? I mean, when I physically look at the diagram, those 2 sides, "a" and "b" are not in the same triangle... I don't know if I'm clearly explaining myself here...
What happens to the other 2 sides that aren't labelled?