Question

AC=CE and D is the midpoint of CE. If CE = 10x+18 DE = 7x-1 and BC = 9x-3 find AB

Answer 1

We know the CE = 10x + 18 and DE = 7x - 1 and D is the midpoint of CE

⇒ CE = 2 * DE

⇒ 10x + 18 = 2 * (7x - 1)

⇒ 10x + 18 = 14x - 2

⇒ -4x = -20

⇒ x = 5

Now we also know that BC = 9x - 3 and AC = CE = 10x + 18

⇒ AB = AC - BC

⇒ AB = 10x + 18 - (9x - 3)

⇒ AB = x + 21

Substituting the value of x,

⇒ AB = 5 + 21

⇒ AB = 26

Hence, the value of AB is 26 units.