Find the value of x in the figure?

enter image source here

2 Answers
Aug 6, 2016

In Fig.(a), x=8.75

In Fig.(b), x8.57

Explanation:

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, x7=8+28x=708=8.75

In Fig.(b), #x/15=12/21 rArr x=180/21~=8.57

Aug 6, 2016

In Figure (a): x=834

In Figure (b): x=847

Explanation:

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:
enter image source here
Notice the similar triangles:
XXXABC~ADE

XXX|BC||AB|=|DE||AD|

XXX78=x8+2

XXX8x=70

XXXx=868=834

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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:
enter image source here

PQR~PST

XXX|QR||PQ|=|ST||PS|

XXXx12=159+12

XXX21x=15×12

XXXx=18021=847