Answer:
175.5 cm.
Explanation:
Since the triangles XYZ and LNM are similar, we know that their corresponding sides are proportional. Specifically, we have:
XY / LN = XZ / LM = YZ / NM
Substituting in the given lengths, we have:
XY / 25 = XZ / 20 = YZ / 15
Multiplying by the lowest common denominator of 300, we get:
12XY = 15XZ = 20YZ
Let's use the first equation to solve for XY:
XY = (15/12) XZ = (5/4) XZ
Now, let's use the third equation to solve for YZ:
YZ = (12/20) XZ = (3/5) XZ
Finally, we can use the fact that the perimeter of triangle XYZ is the sum of its side lengths:
Perimeter of XYZ = XY + YZ + XZ
= (5/4) XZ + (3/5) XZ + XZ
= (39/20) XZ
To find XZ, we can use the second equation:
XZ / 20 = XY / 25
XZ = (20/25) XY
XZ = (4/5) XY
XZ = (4/5) (5/4) YZ
XZ = YZ
So, XZ = YZ = (3/5) XZ.
Substituting this into the expression for the perimeter of XYZ, we have:
Perimeter of XYZ = (39/20) XZ
= (39/20) (3/5) YZ
= (117/100) YZ
= (117/100) (15)
= 175.5 cm
Therefore, the perimeter of triangle XYZ is 175.5 cm.