find the value of x of given figure and solve this question step by step plzz help question number D

The value of x is 15 cm

Step-by-step 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

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