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Answer:
x = 7.5
Step-by-step explanation:
Dilation is a transformation in which the size of a given figure is either increased or decreased by a scale factor.
Given that the length of sides of the smaller triangle are; 5, 13, 12.
Given also that the length of the dilated triangle are; x, blank, 18.
Comparing the length of the last sides of the two triangles, we have;
(scale factor x 12) + 12
= ( x 12) + 12
= 6 + 12
= 18
Thus the scale factor for the dilation is . So that:
x = ( x 5) + 5
= 2.5 + 5
= 7.5
x = 7.5
And also,
blank = ( x 13) + 13
= 6.5 + 13
blank = 19.5
Therefore, the length of the sides of dilated triangle are: 7.5, 19.5, 18