Question

已知△ABC中∠C=90°,斜边为c,两直角边为a、b,若△ABC面积记为S,周长记为L.若a+b-c=m 观察下表来猜

Answer 1

S/L=（ab/2)÷(a+b+c)

=ab/2(m+2c)

a+b-c=m

即(a+b）²=(m+c)²

a²+b²+2ab=c²+2cm+m²

因a²+b²=c²

得ab=m(2c+m)/2

所以S/L =ab/2(m+2c)

=m(2c+m)/4(m+2c)

=m/4