Question

The polygons are similar, but not drawn to scale. Find the value of x.

Please explain and answer! :)

Answer 1

`\boxed{x=9}`

Explanation:

The given polygons are similar.

This implies that the corresponding sides of the polygons are proportional.

We can therefore write the following equation of proportion and solve to find the value of
`x`.

`(x-1)/(16)=(6)/(12)`

Let us simplify the fraction on the right hand side to obtain;

`(x-1)/(16)=(1)/(2)`

`(x-1)/(16)=(1)/(2)`

We cross multiply to get;

`2(x-1)=16(1)`

`\Rightarrow 2(x-1)=16`

Divide through by 2 to get;

`\Rightarrow x-1=8`

Make x the subject;

`\Rightarrow x=8+1`

`\Rightarrow x=9`