Question

The smaller triangle was dilated to form the larger triangle. What is the value of x? A smaller triangle has side lengths of 5, 13, 12. A larger triangle has side lengths of x, blank, 18. 6.9 7.5 10 11

Answer 1

7.5

Step-by-step explanation

CUZ IMMA BIG BRAIN

Answer 2

x = 7.5

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

= (
`(1)/(2)` x 12) + 12

= 6 + 12

= 18

Thus the scale factor for the dilation is
`(1)/(2)`. So that:

x = (
`(1)/(2)` x 5) + 5

= 2.5 + 5

= 7.5

x = 7.5

And also,

blank = (
`(1)/(2)` x 13) + 13

= 6.5 + 13

blank = 19.5

Therefore, the length of the sides of dilated triangle are: 7.5, 19.5, 18