Question

Please I need this answer

Answer 1

FE = 12

DE = 20

Explanation:

Part A

We can solve for FE by equating the ratios of the triangles' sides. Remember we can only do this because the triangles are similar, so the scale factor between the side lengths is the same.

`HE : GH = FE : DF`

↓ plugging in the given values

`9 : 12 = FE : 16`

↓ representing as fractions

`(9)/(12) = (FE)/(16)`

↓ multiplying both sides by 16

`\boxed{FE = 12}`

Part B

We can solve for DE using the same technique.

`GE : GH = DE : DF`

↓ plugging in the given values

`15 : 12 = DE : 16`

↓ representing as fractions

`(15)/(12)= (DE)/(16)`

↓ multiplying both sides by 16

`\boxed{DE = 20}`