contestada

A, B, C and D are four points marked in order on a line such that AB : AC = 3 : 7 and BD : CD = 9 : 2. If CD is 100 cm long, find the length of AB.

Respuesta :

calculista

we know that

AB : AC = 3 : 7 and BD : CD = 9 : 2

so

AB/AC=3/7

AC=AB+BC

AB/(AB+BC)=3/7-----> equation 1

BD/CD=9/2-----> equation 2

CD=100 cm-----> substitute in the equation 2

 

BD/100=9/2-----> 2*BD=100*9-----> divide by 2 both sides----> BD=900/2

BD=450 cm

BD=BC+CD----à BC=BD-CD---à BC=450-100--à BC=350 cm

 

Equation 1

AB/(AB+BC)=3/7---à AB/(AB+350)=3/7

7*AB=3*(AB+350)

7*AB=3*AB+1050

4*AB=1050

AB=1050/4

AB=262.5 cm

 

the answer is

the length of AB is 262.5 cm