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
∴ [tex]\frac{PS}{PQ}[/tex] = [tex]\frac{SR}{RQ}[/tex]
∵ 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
∴ [tex]\frac{x}{30}[/tex] = [tex]\frac{40-x}{45}[/tex]
→ 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
