Triangle DEF is similar to triangle PQR. Side DE measures 3, side EF measures 7 and side FD measures 9. Side PQ measures 5x – 25 and side QR measures 6x + 4. Find the value of x.

DE/PQ = 3/(5x -25) = EF/QR = 7/(6x + 4)

18x + 12 = 35x -175

17x = 187
x = 11

DEF has 1/10 the corresponding side lengths of PQR

To find the value of x, we can set up a proportion using the corresponding sides of the two similar triangles. A proportion is an equation that states that two ratios are equal.

In this case, we can set up the proportion using the corresponding sides DE/PQ and EF/QR from the two triangles. The proportion would be:

DE/PQ = EF/QR

Plugging in the given values, we have:

3/(5x – 25) = 7/(6x + 4)

Now, we can solve this proportion for x by cross-multiplying. This means multiplying the numerator of the left side by the denominator of the right side, and vice versa.

Cross-multiplying, we get:

3(6x + 4) = 7(5x – 25)

Simplifying both sides, we have:

18x + 12 = 35x – 175

Next, we can solve for x by isolating the variable terms and simplifying the equation. Subtracting 18x from both sides, we get:

12 = 17x – 175

Adding 175 to both sides, we get:

187 = 17x

Finally, we divide both sides by 17 to solve for x:

x = 187/17

Thus, the value of x is approximately 11.

To find the value of x, we need to use the property of similar triangles that states that corresponding sides of similar triangles are proportional.

In this case, we can set up a proportion using the sides of the triangles:

DE/PQ = EF/QR

Substituting the given values:
3/(5x - 25) = 7/(6x + 4)

Cross-multiplying:
3(6x + 4) = 7(5x - 25)

Expand both sides:
18x + 12 = 35x - 175

Rearrange the equation:
35x - 18x = 175 + 12

Combine like terms:
17x = 187

Divide both sides by 17 to solve for x:
x = 187/17

The value of x is approximately 11.