triangle question

Question

Triangle ABC is an isosceles triangle with segment AC congruent to segment BC. If AB is three more than x, BC is 17 less than four times x and AC is 45 less than six times x, find x and the measures of each side.

Answer 1

Draw and label a diagram

The two sides are equal. Set expressions equal and solve for x and answer.

Answer 2

Sides of Isosceles Triangle ABC: AB, AC, BC (with AC = BC)

Side AB = x + 3

Side BC = 4x - 17

Side AC = 6x - 45

AC = BC ==> 6x - 45 = 4x - 17 ==> 6x - 4x = 45 - 17 ==> 2x = 28 ==> x = 14

Side AB = x + 3 ==> AB = 14 + 3 ==> AB = 17

Side BC = 4x - 17 ==> BC = 4(14) - 17 ==> BC = 56 - 17 ==> BC = 39

Side AC = 6x - 45 ==> AC = 6(14) - 45 ==> AC = 84 - 45 ==> AC = 39

Sides of this Isosceles Triangle ABC are: AB = 17, AC = BC = 39

Answer 3

Triangle ABC is an isosceles triangle with segment AC congruent to segment BC. If AB is three more than x, BC is 17 less than four times x and AC is 45 less than six times x, find x and the measures of each side.

ab=3+x

bc=ac=4x-17

ac=bc=6x-45

2x=28

check, 56-17=

84-45=