Answer:
Given the two triangles are shown:
First triangle has sides x cm , 6 cm and 12 cm.
and
Second triangle has sides 20 cm , 8 cm and 16 cm.
Since, the given two triangles are Similar.
⇒there corresponding sides are in proportion.
i,e
![\frac{x}{20}=\frac{6}{8}=\frac{12}{16}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B20%7D%3D%5Cfrac%7B6%7D%7B8%7D%3D%5Cfrac%7B12%7D%7B16%7D)
(a)
![\frac{x}{20}=\frac{12}{16}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B20%7D%3D%5Cfrac%7B12%7D%7B16%7D)
Solve for x;
By cross multiply we have;
![16x = 240](https://tex.z-dn.net/?f=16x%20%3D%20240)
Divide both sides by 16 we get;
cm
(b)
Find x using the ratio sides:
![\frac{6}{8} = \frac{x}{20}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B8%7D%20%3D%20%5Cfrac%7Bx%7D%7B20%7D)
By cross multiply we have;
![120 = 8x](https://tex.z-dn.net/?f=120%20%3D%208x)
Divide both sides by 8 we get;
or
cm
The value of x =15 cm in both a and b is same because the given two triangles are similar,
by definition of similarity, the given triangles have their corresponding sides are in proportion.