Question #bd22c

2 Answers
Apr 6, 2017

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

Apr 6, 2017

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#