By applying definition of ratios, the ratios associated to each pair of lengths:
- NR : NW = 2 / 5 : 1
- RT : WH = 2 / 5 : 1
- RT : KX = 3 / 8 : 1
How to determine ratios from a geometric system
In this problem we have the case of a geometric system generated by three proportional triangles, of which we must derive the length of ratio related to two similar sides. First, we determine the lengths of each line segment:
NR = √(2² + 2²)
NR = 2√2
NW = √(5² + 5²)
NW = 5√2
RT = 6
WH = 15
KX = 24
Lastly, we calculate the ratios associated with each pair of lengths according to the definition of ratio:
NR : NW = 2√2 : 5√2
NR : NW = 2 / 5 : 1
RT : WH = 6 : 15
RT : WH = 2 : 5
RT : WH = 2 / 5 : 1
RT : KX = 6 : 24
RT : KX = 3 : 8
RT : KX = 3 / 8 : 1
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