triangle QRS ~ triangle EFG. Find the measures of the missing sides.

QR = ? EF = 10
QS = 24 EG = 5
RS = 45 FG = ?

Im having trouble setting up the equations. Please help!!

The ratio is clearly 24:5. So,

QR:10 = 24:5
45:FG = 24:5

To set up the equations for the given similarity of triangles QRS ~ EFG, we can use the corresponding side lengths.

Since QR and EF are corresponding sides, we can create the proportion:

QR/EF = QS/EG

Substituting the given values, we have:

QR/10 = 24/5

Now, we can solve for QR.

Cross-multiplying, we get:

5 * QR = 10 * 24

5QR = 240

Dividing both sides by 5, we find:

QR = 48

Next, we can use the same process to find the missing side RS.

RS/FG = QS/EG

Substituting the given values, we have:

RS/FG = 24/5

Now, we can solve for RS.

Cross-multiplying, we get:

5 * RS = 24 * FG

5RS = 24FG

Dividing both sides by 5, we find:

RS = 4.8FG

Finally, we are given that RS = 45. Therefore, we can substitute this value into the equation:

45 = 4.8FG

Now, we can solve for FG.

Dividing both sides by 4.8, we find:

FG = 45/4.8

Simplifying, we get:

FG ≈ 9.375

So, the measures of the missing sides are:

QR = 48
FG ≈ 9.375

To set up the equations for finding the measures of the missing sides in the similar triangles QRS and EFG, we can use the concept of ratio of corresponding sides.

In similar triangles, corresponding sides are proportional. This means that the ratio of the lengths of corresponding sides in the two triangles will be equal.

In the given problem, we are given the lengths of EF and EG, and we need to find the lengths of QR and FG.

Let's set up the equation using the ratio of corresponding sides:

QR / EF = QS / EG

Substituting the given values:

QR / 10 = 24 / 5

Now, we can cross-multiply and solve for QR:

QR * 5 = 10 * 24
QR = (10 * 24) / 5

QR = 48

So, the length of QR is 48.

Similarly, we can set up the equation for the other pair of corresponding sides:

RS / EF = QS / FG

Substituting the given values:

45 / 10 = 24 / FG

Now, we can cross-multiply and solve for FG:

45 * FG = 10 * 24
FG = (10 * 24) / 45

FG ≈ 5.33

So, the length of FG is approximately 5.33.

Therefore, the measures of the missing sides are:
QR = 48 (units)
FG ≈ 5.33 (units)