Question

What is the length of 

Answer 1

Answer:

In first picture,

m∠C = m∠B

⇒ AC = AB

⇒ x + 9 = 2x - 8

⇒ x - 2x = -8 - 9

⇒ -x = -17

⇒ x = 17

Hence, the length of BC = x = 17 units,

In second picture,

m∠A = m∠B = m∠C

⇒ Triangle ABC is an equilateral triangle,

⇒ AB = BC = CA

⇒ 4x - 10 = 5x - 22 = 3x + 2

When,

⇒ 4x - 10 = 5x - 22

⇒ 4x - 5x = -22 + 10

⇒ -x = -12

⇒ x = 12

Hence, the value of x is 12.

In third picture,

LN = LM = NM

The triangle LMN is an equilateral triangle,

⇒ m∠L = m∠M = m∠N = 60°

⇒  m∠L= 60°

⇒ 7x - 3 = 60

⇒ 7x = 63

⇒ x = 9

Hence, the value of x is 9.