Question

Triangle ABC is isosceles with AB and AC congruent to each other. If AB = 21x - 14, BC = 35x - 14 and AC = 14x + 7. solve for x and determine the length of all sides.

Answer 1

Since the isosceles triangle has AB=AC, and we're given

AB=21x-14

AC=14x+7

we can equate

AB=AC

21x-14=14x+7

Solve for x

21x-14x = 7+14

7x=21

x=3

=> AB=21x-14=63-14=49 units

=> AC=14x+7=42+7=49 units

=> BC=35x-14 = 105-14=91 units

and since 49+49>91 units, the lengths satisfy the triangle inequality.