Question

In the figure ∟D=900 , AB=16cm , BC=12cm, CA= 6cm then CD is
(a) 75/8
(b) 19/6
(c) 20/7
(d) 25/8​

Answer 1

Given :  AB=16cm , BC=12cm, CA= 6cm  

∠D = 90°

To Find :  CD

(a) 75/8

(b) 19/6

(c) 20/7

(d) 25/8​

Solution:

Let say CD = x

Using Pythagoras theorem :

AD² = AC² - CD²

=> AD²  = 6² - x²

AD²  = AB² - BD²

=> AD² = 16²  - (BC + CD)²

=> AD² = 16² - (12 + x)²

Equate AD²

6² - x² =  16² - (12 + x)²

=> 36 - x² =  256 -  ( 144 + x²  + 24x)

=>  24x  = 256 - 144 - 36

=> 24x =  76

=> x = 76/24

=> x = 19/6

Hence correct option is option (b) 19/6

Learn More:

using the concept of Pythagoras theorem construct a segment of ...

brainly.in/question/8399081

draw a tangent segment of length √12 cm the circle with centre o ...

brainly.in/question/13741684

Answer 2

Answer:

The length of the CD is $\frac{19}{6}$

Step-by-step explanation:

Given:

Angle D is $90^0$

$AB=16cm\\\\BC=12cm\\\\CA=6cm$

We need to find CD

By applying Pythagoras theorem to Triangle ADC

We get

$AD^2=AC^2-CD^2\\\\AD^2=36-CD^2$--$1$

By applying Pythagoras theorem to Triangle ADB

$AD^2=AB^2-(DC+12)^2\\\\AD^2=256-(DC+12)^2$--$2$

Let $CD=x$

By equating $1$ and $2$ we get

$36-CD^2=256-(DC+12)^2\\\\(DC+12)^2-CD^2=256-36\\\\x^2+24x+144-x^2=220\\\\24x=76\\\\x=\frac{19}{6}$