Question

Question #bd22c

Answer 1

This can be solved by using Pythagorean theorem

Explanation:

To find x you must find DC and to do this you can use Pythagorean theorem

`a^2 + b^2 = c^2`
`2.25^2 + b^2 = 3^2`
`5.0625+ b^2 = 9`
`5.0625 - 5.0625+ b^2 = 9-5.0625`
`b^2=3.9375`
`sqrtb^2=sqrt3.9375`
`b = 1.984`

1.984 is the value of Dc

Same thing for X

`a^2 + b^2 = c^2`
`1.984^2 + b^2 = 4^2`
`3.9375 + b^2 = 16`
`3.9375 - 3.9375 + b^2 = 16 -3.9375`
`b^2 = 12.064`
`sqrtb^2 = sqrt12.064`
`b = 3.473`

3.473 is the value of x

Answer 2

Assuming I understand the intent of the diagram:
`color(white)("XXX")x=3`

Explanation:

If the diagram is intended to show that `/_ACD =/_DCB`
then by the Angle Bisector Theorem
`color(white)("XXX")abs(AD)/abs(AC)=abs(DB)/abs(CB)`

Replacing with values shown on the diagram:
`color(white)("XXX")(2.25)/3=x/4`

`color(white)("XXX")rarr 9/3=x`

`color(white)("XXX")rarr x=3`