Question

IF AB = x+3, BC = 2x and AC = 4x - 5 then what is the value of x, B lies on AC ?

a. 2
b. 3
c. 5
d. 8

Answer 1

AB = x + 3

BC = 2x

AC = 4x - 5

AB + BC + AC = 180

x + 3 + 2x + 4x - 5

Answer 2

Answer :

›»› The value of x is 8.

Given :

• AB = x + 3.
• BC = 2x
• AC = 4x - 5

To Find :

• The value of x.

Solution :

If B lies on AC. So,

→ AB + BC = AC

→ (x + 3) + (2x) = (4x - 5)

→ x + 3 + 2x = 4x - 5

→ x + 2x + 3 = 4x - 5

→ 3x + 3 = 4x - 5

→ 3x + 3 - 4x = -5

→ 3x - 4x = -5 - 3

→ -1x = -5 - 3

→ -x = -5 - 3

→ -x = -8

→ x = 8

Hence, the value of x is 8.

Correct option is (d) 8 ✔.

Verification :

→ AB + BC = AC

→ (x + 3) + (2x) = (4x - 5)

→ (8 + 3) + (2 * 8) = (4 * 8 - 5)

→ 11 + (2 * 8) = (4 * 8 - 5)

→ 11 + 16 = (4 * 8 - 5)

→ 11 + 16 = 32 - 5

→ 27 = 32 - 5

→ 27 = 27

Here, LHS = RHS

Hence Verified !