Question

RT三角形ABC中,若a∶b=3∶4,c=10,则三角形ABC的面积为?

Answer 1

第一种情况:c为斜边

a^2+b^2=c^2

a:b=3:4 所以设a=3x b=4x

(3x)^2+(4x)^2=c^2=100

9x^2+16x^2=100

x^2=4

x=2

a=6 b=8 S=1/2*6*8=24

第二种情况: b为斜边

设a=3x b=4x

(3x)^2+10^2=(4x)^2

9x^2+100=16x^2

7x^=100

x^2=100/7

x=10/7根号7 a=30/7根号7

S=1/2*30/7根号7*10

=150/7根号7