Question

∆ABC is a right-angled triangle, right angled at B and BD ⊥ AC. If BD = 10cm, AB = 5 cm and BC = 5 cm then AC will be?

(a) 44.72 cm

(b) 5.59 cm

(c) 18.11 cm

(d) 22.36 cm

This question was posed to me by my college director while I was bunking the class.

My enquiry is from Pythagoras Theorem in section Triangles of Mathematics – Class 10

Answer 1

Right option is (d) 22.36 cm

The explanation is: The figure according to the given data is:

BD = 10cm and AB = 5cm

Now, in ∆ADB

AD^2 = AB^2 + BD^2

AD^2 = 5^2 + 10^2

AD^2 = 25 + 100

AD^2 = 125

AD = √125 = 11.18 cm

Now, in ∆ABD and ∆CBD

BD = BD     (Common Side)

∠ADB = ∠CDB     (Both 90°)

AB = BC     (Given)

∆ABD ≅ ∆CDB (RHS Congruency)

Therefore, AD = DC

AC = AD + DC = 2AD = 2 × 11.18cm = 22.36cm