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21. The two triangles below are similar. What is the perimeter of triangle XYZ? Y M 20 cm L 25 cm 15 cm X N 2 6 cm Z​

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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.

User Brian Gradin
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