Question

In ΔABC, ∠BAC = 90° = ∠APB. BC = 85 cm, AC = 75 cm and BP = 32 cm. Find x and y.

Answer 1

In ΔABC, ∠BAC = 90° = ∠APB. BC = 85 cm, AC = 75 cm and BP = 32 cm.

Find x and y.

x = AB

y = PC

Step 1: Use Pythagoras theorem in ΔABC:

Since ∠A = 90°, we apply:

BC² = AB² + AC²

⇒ 85² = x² + 75²

7225 = x² + 5625

⇒ x² = 1600

⇒ x = `sqrt(1600)`

⇒ x = 40 cm

Step 2: Use Pythagoras theorem in ΔBAP:

∠APB = 90°  ....(Right angle at P.)

⇒ AB² = AP² + BP²

40² = y² + 32²

⇒ 1600 = y² + 1024

⇒ y² = 576

⇒ y = `sqrt(576)`

⇒ y = 24 cm