中二數學一條【求完整解答及說明】

(a) :
Method I :
Let BC be k cm, AB be 3/4k, k≠0,
(3/4k)^2+k^2=30^2 (Pyth. theorem)
(9k^2)/16+k^2=900
(25k^2)/16=900
k^2=576 <-- (900*16/25=576)
k=24

BC=24 cm

AB=3/4(24)
=18 cm

Method II :
Let BC be k cm, AB be 3/4k, k≠0,
√((3/4k)^2+k^2)=30 (Pyth. theorem)
√((9k^2)/16+k^2)=30
√((25k^2)/16)=30
√(5k)/4=30
k=24 <-- (30*4/5=24)

BC=24 cm

AB=3/4(24)
=18 cm

(b) : perimeter=18+24+30=72 cm

*perimeter=周界*