Question

in a trianle abc angle b is 90 degree bd perpendicular to ac. bc is 8 cm ad is 4 cm. find cd

Answer 1

Answer:

CD = 6.25 cm

Step-by-step explanation:

if we Draw Triangle

BC = 8 cm

AD = 4cm

AC² = AB² + BC²

AC = CD + AD = CD +4

BC = 8 cm

CD²+16+8CD = AB² + 64

CD² + 8CD = AB² + 48     EQUATION- I

CD² = BC² - BD²

BD² = AB² - AD²

so

CD² =  BC² - AB² + AD²

CD² = 8² - AB² + 4²

CD² = 80 - AB²      

AB² = 80 - CD²      - Equation 2

Now putting AB² from  equation 2 in equation 1

CD² + 8CD = AB² + 48    

CD² + 8CD =  80 - CD² + 48

2CD² + 8 CD =  128

CD² + 4 CD = 64

CD(CD+4) = 64

Solving this we get

CD = 6.25 cm