A figure has a perimeter of 26 units. What will the new perimeter be after dilation with a scale factor of 2.5?

Answer 1

P = 2L + 2w <---- formula for perimeter

26 = 2L + 2w <--- original perimeter is 26

13 = L + w <--- divides everything by 2

32.5 = 2.5L + 2.5w <-- scale factor of 2.5; those are the NEW length and width

Multiplying both sides by 2, the new perimeter is 65;

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Here's another way:

As before, 13 = L + w. So,L = 13 - w

Upon dilation with scale factor of 2.5,

the new width is 2.5w and the new length is 2.5L

So the NEW perimeter is 2(2.5w) + 2(2.5L) =

5w + 5L =

5(w +L) =

5(13) <--- substitution

= 65