Question

In ΔABC, ∠B = 90°, AP = 5, PB = 15, PQ = 17 and QC = 7. Find the values of x and y.

Answer 1

Given,

ΔABC, ∠B = 90°, AP = 5, PB = 15, PQ = 17 and QC = 7.

Pythagoras theorem states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides.

In ΔPBQ,

⇒ PQ² = PB² + BQ²

⇒ 17² = 15² + x²

⇒ 17² – 15² = x²

⇒ x² = 289 – 225 = 64

⇒ x = `sqrt(64)` = 8 cm

And in ΔABC,

⇒ AC² = AB² + BC²

⇒ y² = 20² + 15²

⇒ y² = 400 + 225 = 625

⇒ y = `sqrt(625)` = 25 cm

Hence, this is required.