Question

I need help with this question.

The choices are:
A). x=7
B). x=11
C). x=23.57
D). x=8.57

Answer 1

D.
`x=8.57`

Explanation:

We can see from our graph that triangle CED is similar to triangle CBA. Side length BA corresponds to ED and Side length AC corresponds to DC.

Since we know that corresponding sides of two similar triangle are in the same proportion. To find value of x we will set proportion of the corresponding sides of our given triangles equal.

`(x+15)/(15) =(11)/(7)`

Upon cross multiplying our given equation we will get,

`7(x+15)=11* 15`

Upon distributing 7 we will get,

`7x+105=11* 15`

`7x+105=165`

`7x=165-105`

`7x=60`

`x=(60)/(7)`

`x=8.5714285714285714\approx 8.57`

Therefore, x equals 8.57 and option D is the correct choice.