Question

Find the value of x in the figure?

Answer 1

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

In Fig.(b), `x~=8.57`

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, `x/7=(8+2)/8 rArr x=70/8=8.75`

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

Answer 2

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

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

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:

Notice the similar triangles:
`color(white)("XXX")triangleABC~triangleADE`

`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`