Question

29.In ABC ˪B =900and BC ┴ AC if AC = 10 cms, AB =6 cms, BC = 8 cms,

then CD=________

A) 6.4 cms B) 6.2 cms C) 5.4 cms D) 5.2 cms​

Answer 1

Given info : In ABC, ∠B = 90° , and BD ⊾ AC where AC = 10 cm,. AB = 6 cm and BC = 8 cm

To find : the value of CD is ...

solution : see figure, ∆BDC ,

from Pythagoras theorem, BC² = BD² + CD² ...(1)

for ∆ADB,

from Pythagoras theorem, AB² = BD² + AD²

= BD² + (AC - CD)²

= BD² + AC² + CD² - 2AC.CD

= (BD² + CD²) + AC² - 2AC.CD

from equation (1) we get,

= BC² + AC² - 2AC.CD

⇒(6cm)² = (8cm)² + (10cm)² - 2(10cm) × CD

⇒36 = 64 + 100 - 20 CD

⇒-128 = -20 CD

⇒CD = 6.4 cm

Therefore the value of CD is 6.4 cm