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Flura [38]
3 years ago
12

ΔABC is similar to ΔDEF. The ratio of the perimeter of ΔABC to the perimeter of ΔDEF is 1 : 5. If the longest side of ΔDEF measu

res 15 units, what is the length of the longest side of ΔABC?
Mathematics
1 answer:
PilotLPTM [1.2K]3 years ago
8 0

Answer:

Length of the longest side of ΔABC = 3 units

Step-by-step explanation:

If two similar triangles have a scale factor a:b, then the ratio of perimeters is also a:b.

Here, the converse is applied.

The perimeter of similar triangles is in the ratio 1:5, so, the corresponding lengths are also in the ratio 1:5

Perimeter of ΔABC : Perimeter of ΔDEF = 1:5

Longest side of ΔABC : Longest side of ΔDEF = 1:5

Longest side of ΔABC : 15 = 1:5

∴ Longest side of ΔABC = (1/5) * 15 = 3 units

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