maths F4,help in eqt

Let a cm and b cm be thelengths of the wires respectively. (Assume that a > b)

a - b = 8 ...... [1]
(a/4)² + (b/4)² = 100 ...... [2]

From [1] :
a = b + 8 ...... [3]

Put [3] into [2] :
[(b + 8)/4]² + (b/4)² = 100
(b + 8)² + b² = 1600
b² + 16b + 64 + b² = 1600
2b² + 16b - 1536 = 0
b² + 8b - 768 = 0
(b - 24)(b + 32) = 0
b = 24 or b = -32 (rejected)

Put b = 24 into [3] :
a = 24 + 8
a = 32

Hence, the lengths of the wires are 24 cm and 32 cm respectively.