Theo đề ta có:
AB = $\frac{8}{15}$AC
Theo Pytagoras có: $BC^{2}$ - $AB^{2}$ = $AC^{2}$
=> $AC^{2}$ = $51^{2}$ - ($\frac{8}{15}$) $^{2}$ . $AC^{2}$
<=>$AC^{2}$ = 2601 - $\frac{64}{225}$$AC^{2}$
<=>$\frac{289}{225}$$AC^{2}$ = 2601
<=> AC = 45cm
=> AB = 45 . $\frac{8}{15}$ = 24 cm