Triangle BCD is similar to triangle EFG. Find the measure of side FG.!!! Round your answer to the nearest tenth if necessary
B
C
D
E
F
G
19
30
58
To find the measure of side FG, we must first determine the scale factor between the two similar triangles.
The scale factor can be found by comparing corresponding sides. In triangle BCD, side BC is 30 and side CD is 58. In triangle EFG, side FG corresponds to side CD.
The scale factor from triangle BCD to triangle EFG is 30/58 = 0.5172
Now, to find the measure of side FG, we take the corresponding side from triangle BCD (30) and multiply it by the scale factor:
30 * 0.5172 = 15.516
Therefore, the measure of side FG is approximately 15.5 units.
thats incorrect
I apologize for the mistake. Let's try to solve the problem again.
Since triangle BCD is similar to triangle EFG, we can set up the proportion:
BC/EF = CD/FG
Substitute the given values:
30/EF = 58/FG
Cross multiply:
58EF = 30 * FG
58EF = 30FG
To find the measure of side FG, isolate FG:
58EF = 30FG
FG = 58EF / 30
Now, we need to find the value of EF to solve for FG.
Using the Pythagorean theorem:
EF = √(EG^2 + FG^2)
EF = √(19^2 + 30^2)
EF = √(361 + 900)
EF = √1261
EF ≈ 35.5
Now we can find FG:
FG = 58(35.5) / 30
FG = 2039 / 30
FG ≈ 67.97
Therefore, the measure of side FG is approximately 68 units.