**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

edited by Guest Feb 23, 2018

#1**+1 **

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

CPhill Feb 23, 2018