The length of HI in the similar triangles is: (4) 24.
What are Similar Triangles?
The corresponding sides of triangles that are similar to each other have ratios that are equal to each other, thus, they are proportional.
Triangle EFI and triangle GHI are similar to each other. Therefore, their corresponding sides have ratios that are equal. Thus, we will have the following:
HI/FI = HG/EF
Given:
EF = 5,
HG = 12,
FI = 1.4x + 3
HI = 6.1x - 6.5
Plug in the values
6.1x - 6.5/1.4x + 3 = 12/5
Cross multiply
5(6.1x - 6.5) = 12(1.4x + 3)
Open the bracket
30.5x - 32.5 = 16.8x + 36
30.5x - 16.8x = 32.5 + 36
13.7x = 68.5
Divide both sides by 13/7
13.7x/13.7 = 68.5/13.7
x = 5
HI = 6.1x - 6.5
Plug in the value of x
HI = 6.1(5) - 6.5
HI = 30.5 - 6.5
HI = 24
The length of HI in the similar triangles is: (4) 24.
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