Triangle LMN is similar to triangle XYZ.
The scale factor of triangle LMN to triangle XYZ is 2:5.
What is the length of ZX ?
A 2 units
B 5 units
C 7.5 units
D 12.5 units
Assuming they are both equilateral triangles and LMN sides are 2, the answer would be B.
ZX = 5/2 * NL.
A similar problem says that triangle LMN has sides of 5 and 3.
So ZX = 5/2 * 5 = 12.5 units.
Or ZX = 5/2 * 3 = 7.5 units.
To find the length of ZX, we need to use the scale factor of 2:5 between triangle LMN and triangle XYZ.
Since the scale factor is 2:5, it means that every corresponding length in triangle LMN is multiplied by 2 to get the corresponding length in triangle XYZ.
Let's say the length of ZN in triangle XYZ is x units.
Therefore, the length of MN in triangle LMN is also x units, as both triangles are similar.
According to the scale factor, the length of MN is 2 times the length of ZN.
So, MN = 2x units.
Now, the length of ZX is equal to the length of ZN plus the length of MN.
ZX = x + 2x = 3x units.
Since the scale factor is 2:5, we can set up the following proportion:
2/5 = x/3x
Simplifying the proportion, we get:
2/5 = 1/3
Multiplying both sides of the equation by 3, we get:
3 * 2/5 = 3 * 1/3
6/5 = 1
This is not possible since 6/5 is not equal to 1.
Therefore, it is not possible to determine the length of ZX given the information provided.
To find the length of ZX, we can use the scale factor of the similar triangles, which is 2:5.
Step 1: Identify the corresponding sides in the two triangles. In this case, we are looking for the length of ZX, which corresponds to the side MN in triangle LMN.
Step 2: Set up a proportion using the scale factor. The proportion is:
MN / ZX = LM / XY
Step 3: Substitute the known values into the proportion. We know that the scale factor is 2:5, so LM is 2 units and XY is 5 units. Let's substitute these values into the proportion:
MN / ZX = 2 / 5
Step 4: Solve for the unknown value, which is ZX. Rearrange the proportion to solve for ZX:
ZX = (MN * XY) / LM
Step 5: Plug in the values and calculate ZX:
ZX = (2 * 5) / 2
ZX = 10 / 2
ZX = 5 units
Therefore, the length of ZX is 5 units. The correct answer is option B.