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.

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+CDà 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

Complementary angles are adjacent angles which add to equal 90 degrees (a right angle). To find m∠A in these figures, set the sum of the known angle measure and the unknown angle measure, A, equal to 90 and solve.

10)
90 = 67 + A
23 = A
m∠A = 23°

11)
90 = 57 + A
33 = A
m∠A = 33°

12)
90 = 44 + A
46 = A
m∠A = 46°