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The ratio of two side lenghts for the triangle is given. Solve for varieble. (Answer for today please ^^)

A) AC:AB is 3:4 

B) AB:CB is 2:1

C) AC:BC is 7:4

 

 

A) Tringle ABC has side lenghts:

AC=x

AB=2

 

B) Tringle ABC has side lenghts:

AB=16x

CB=24

 

C) Tringle ABC has side lenghts:

ABC=21

CB=2x+4

Guest Feb 23, 2018
edited by Guest  Feb 23, 2018
edited by Guest  Feb 23, 2018
 #1
avatar+87334 
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AC / AB  =  3 / 4  ⇒  AB  = (4/3)AC

AB / BC  = 2/ 1   =  (1/2)AB = BC ⇒ AB = 2BC

AC / BC  = 7/4 ⇒  AC  = (7/4)BC


A. 

AC   = x

AB  = 2

AB  = (4/3)(AC)

2 = (4/3)x

6/4  = x  = 3/2

 

B.

AB  = 16x

CB  =  24

(1/2)AB  = CB  = BC

(1/2)AB  = 24

(1/2)16x  =  24

8x = 24

x  = 3

 

 

C. ABC  = 21

     BC = 2x + 4

 

This implies that

AB + AC + BC  =  21

Put everything in terms of BC

2BC + (7/4)BC + BC = 21        { sub  2x + 4  for BC }

 

2 (2x + 4)  + (7/4)(2x + 4)  + (2x + 4)  = 21

4x + 8  + (7/2)x + 7 + 2x + 4  = 21

(19/2)x + 19  = 21

(19/2)x  = 2

x  = (2/19) * 2   =  4/19

 

Proof :

BC   =  8/19 + 4  =  84/ 19  

AC  = (7/4)BC = (7/4)(84/19)  = 147/19  

AB = 2BC = 2(84/19)  =  168/19

 

(84 + 147 + 168)  / 19  =  21

 

 

 

 

 

cool cool cool

CPhill  Feb 23, 2018
 #3
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thank U!! ur thebest phill

Guest Feb 23, 2018
 #2
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A)  x =1.5

 

B) x=3

 

C) not sure but maybe x = -2

 

maybe misunderstood the question so ignore answers

Guest Feb 23, 2018
edited by Guest  Feb 23, 2018

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