Method of False Position Question

 

Q1) Let the base of the right triangle is one-third larger than the height. Let 75cm be the length of the diagonal. Find the base and height of the right triangle?


Sol)

Assume that the height is 30cm.

By using the Pythagorean Theorem, we can get the diagonal of the triangle:


d= sqrt(30^2+40^2) = 50 cm

 

50 is 50/75 (=2/3) times of the actual length of the diagonal, so the actual dimensions of the base and height should be 3/2 times of that of assumption.

 

Height = 30 x 3/2 = 45 cm

Base = 40 x 3/2 = 60 cm

 




Q2) Solve the following linear system by using the ancient Egyptian algebraic method of false position.

 

3x + 7y = 350 ------ (1)

5x – 2y = 310 ------ (2)

 

Select the false value x’=y’, which implies by equation (1) 3x’+7x’= 10x’=350

 

è x’ = 35

 

Then modify the false value as follow:

 

è x = x’ + 7f

x = 35 + 7f

 

è y = y’ - 3f

y = 35 - 3f

 

(f cancel out when it is replaced in equation (1))

 

Now replace them in equation (2)

è 5 (35 + 7f) – 2 (35 - 3f) = 105 + 41f = 310

 

Therefore,

x = 35 + 7 (5) = 70

y = 35 – 3 (5) = 20

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