Question

If triangle CDE ~ triangle FGE find the value of x

Answer 1

In the similar triangles CDE and FGE, the ratio of CE to EF is 27 to x, and the ratio of DE to EG is 25 to 40. Solving for x yields a value of 43.2.

Since triangles CDE and FGE are similar, the corresponding sides are in proportion. Therefore, we can set up the ratios:

`1. \( (CE)/(EF) = (27)/(x) \)\\2. \( (DE)/(EG) = (25)/(40) \)`

From the second ratio, simplify by dividing both sides by 5:

`\[ (DE)/(EG) = (5)/(8) \]`

Now, since the sides CE and DE correspond, and EF and EG correspond, we can set up an equation:

`\[ (CE)/(EF) = (DE)/(EG) \]`

Substitute the given values:

`\[ (27)/(x) = (5)/(8) \]`

Now, solve for x:

`\[ x = (27 * 8)/(5) = 43.2 \]`

So, the value of x is 43.2.

The complete question is:
if triangle CDE ~ triangle FGE find the value of x. The image is attached.