Figure PQRS shows the top view of a square box. The length of diagonal PR is (x + 6) units and the length of diagonal QS is (3x – 1) units.

Which property of squares is used to write the equation (x + 6) = (3x – 1) and solve for x?

Question

Figure PQRS shows the top view of a square box. The length of diagonal PR is (x + 6) units and the length of diagonal QS is (3x – 1) units.  
 

 
Which property of squares is used to write the equation (x + 6) = (3x – 1) and solve for x?

anonymous · Answer

Firstly, its a square box. That means it has all 4 90 degree angles. This then makes it so that both diagonals MUST be equal. In other words, (x+6) = (3x-1).

Then $$x + 6 = 3x - 1 \rightarrow 7 = 2x \rightarrow x = { 7 \over 2 }$$