7. Consider the similar trianges below.
Part A:
The first triangle is, S, 5, 7, R, 8, T and the second triangle is, B, 14, C, A.
Find the scale factor.
The scale factor is: ____
Part B
Find the length of AC.
The length of AC is ____
whole numbers only!!
Part A:
To find the scale factor, we can compare the corresponding sides of the two triangles.
In triangle SRT, the side SR has a length of 5, and in triangle BCA, the corresponding side BC has a length of 14.
So, the scale factor is given by:
Scale factor = Length of BC (triangle BCA) / Length of SR (triangle SRT)
Scale factor = 14 / 5
Scale factor = 2.8
Part B:
Since we have found the scale factor to be 2.8, we can use it to find the length of AC.
In triangle SRT, the side ST has a length of 8, and in triangle BCA, the corresponding side CA has a length of A (to be determined).
So, the length of AC is given by:
AC = Length of ST (triangle SRT) * Scale factor
AC = 8 * 2.8
AC = 22.4
Therefore, the length of AC is 22.