Answer:
The value of x is 15 cm
Explanation:
#(d)
In Δ BDC
∵ ∠D is a right angle
∴ BC is the hypotenuse
∴ BD and DC are the legs of the right angle
→ By using Pythagoras Theorem
∵ (BC)² = (BD)² + (DC)²
∵ BD = 10 cm
∵ DC = 2√11 cm
→ Substitute them in the equation above
∴ (BC)² = (10)² +(2√11)² = 100 + 44 = 144
→ Take √ for both sides
∴ BC = 12 cm
In Δ ABC
∵ ∠B is a right angle
∴ AC is the hypotenuse
∴ AB and BC are the legs of the right angle
→ By using Pythagoras Theorem
∵ (AC)² = (AB)² + (BC)²
∵ AB = 9 cm
∵ BC = 12 cm
∵ AC = x
→ Substitute them in the equation above
∴ x² = (9)² +(12)² = 81 + 144 = 225
→ Take √ for both sides
∴ x = 15 cm
∴ The value of x is 15 cm