Which is subsequently the ratio of the perimeter of ΔDEF to that of ΔABC.

Refer to the above figure. Given that ΔABC ~ ΔDEF, give the perimeter of ΔDEF.

A. 135
B. 306
C. 208
D. 324
E. 225

Correct Answer: E
Explanation/Reference:
Explanation:
By the Pythagorean Theorem,




=12
The similarity ratio of ΔDEF to ΔABC is

, which is subsequently the ratio of the perimeter of ΔDEF to that of ΔABC.
The perimeter of ΔABC is AB + BC + AC = 5 + 12 + 13 = 30, so the perimeter of ΔDEF can be found using this ratio:


Perim ΔDEF = 7.5 × 30 = 225

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