Triangle EFG is similar to triangle HIJ. Find the measure of side IJ. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.
E
F
G
H
I
J
7
12
33
Answer
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To find the measure of side IJ, we need to use the properties of similar triangles. Since triangle EFG is similar to triangle HIJ, their corresponding sides are proportional.
The ratio of EF to HI is 7:33, which simplifies to 1:4. This means that the scale factor from triangle EFG to triangle HIJ is 1:4.
Since side FG is 12 in triangle EFG, we can find the length of side IJ by multiplying 12 by the scale factor of 4.
12 * 4 = 48
Therefore, the measure of side IJ is 48.
that answer isnt correct
I apologize for the error. Let's reevaluate the problem:
Given:
EF = 7
FG = 12
HI = 33
Since triangle EFG is similar to triangle HIJ, their corresponding sides are proportional. Therefore, we can set up the following proportion:
EF / HI = FG / IJ
Substitute the given values:
7 / 33 = 12 / IJ
Cross multiply:
7 * IJ = 33 * 12
7IJ = 396
Divide by 7:
IJ = 396 / 7
IJ = 56
Therefore, the measure of side IJ is 56.
are you sure?
Let's recheck the calculations:
Given:
EF = 7
FG = 12
HI = 33
Since triangle EFG is similar to triangle HIJ, their corresponding sides are proportional. Therefore, we can set up the following proportion:
EF / HI = FG / IJ
Substitute the given values:
7 / 33 = 12 / IJ
Cross multiply:
7 * IJ = 33 * 12
7IJ = 396
Divide by 7 to solve for IJ:
IJ = 396 / 7
IJ = 56
Therefore, after recalculating, the measure of side IJ is indeed 56.