Find the value of x in the figure?

Question

Aurora Ayala · Accepted Answer

In Figure (a): #color(green)(x=8 3/4)#

In Figure (b): #color(green)(x=8 4/7)#

Figure (a)
I have assumed that the lines labelled with #7# and #x# are parallel (otherwise this question can not be solved).
Reproducing the figure (a) with labelled vertices for reference purposes:
#rarrcolor(white)("XXX")abs(BC)/abs(AB)=abs(DE)/(abs(AD)#

#rarrcolor(white)("XXX")7/8=x/(8+2)#

#rarrcolor(white)("XXX")8x=70#

#rarrcolor(white)("XXX")x=8 6/8 = 8 3/4#

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Figure (b)
Similarly in figure (b) I have had to assume that sides with lengths #15# and #x# are parallel.
Again, reproducing the image with labelled vertices:

#trianglePQR ~ trianglePST#

#rarrcolor(white)("XXX")abs(QR)/abs(PQ)=abs(ST)/abs(PS)#

#rarrcolor(white)("XXX")x/12 = 15/(9+12)#

#rarrcolor(white)("XXX")21x=15xx12#

#rarrcolor(white)("XXX")x=180/21 = 8 4/7#

Savannah Aguilar · Answer

In Fig.(a), #x=8.75#

In Fig.(b), #x~=8.57# In Similar Triangles, the corresponding sides are in proportion. In Fig.(a), the small triangle ling inside the big one is similar to each other. Hence, #x/7=(8+2)/8 rArr x=70/8=8.75# In Fig.(b), #x/15=12/21 rArr x=180/21~=8.57