Comment The two triangles (ABC and ADE) can be shown to be similar (which I'll do below). Their corresponding parts are also similar. Step One Prove Similarity. A is common to both triangles Construction <ABC = <ADE Given as right angles.
By the AA Theorem both triangles are similar.
Step Two Find x
AD is to AB as DE is to x AD = 3 + 4 = 7 AB = 3 DE = 6 7 / 3 = 6/x Cross multiply 7x = 3 * 6 7x = 18 Divide by 7 x = 18/7 x = 2.571 <<<<< answer
The pattern is: ( a - b )² = a² - 2 a b + b² ( square of last term of binomial - the missing term) x² - 2 · 8 · x + 8² = x² - 16 x + 64 = ( x - 8 )² The missing term is: 64
