Question

QS is an angle bisector, what is the value of x?

Answer 1

Answer:

The value of x is 16

Step-by-step explanation:

The angle Bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle

In Δ QPR

∵ QS is the angle bisector

∵ PR is the opposite side

→ By using the rule above

∴ $\frac{PS}{PQ}$ = $\frac{SR}{RQ}$

∵ PS = x and PQ = 30

∵ PR = 40

∵ RS = PR - PS

∴ RS = 40 - x

∵ RS = 40 - x and RQ = 45

→ Substitute them in the rule above

∴ $\frac{x}{30}$ = $\frac{40-x}{45}$

→ By using the cross multiplication

∵ x × 45 = 30 × (40 - x)

∴ 45x = 30(40) - 30(x)

∴ 45x = 1200 - 30x

→ Add 30x to both sides

∵ 45x + 30x = 1200 - 30x + 30x

∴ 75x = 1200

→ Divide both sides by 75

∴ x = 16

∴ The value of x is 16