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
+128475 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
