Question

Could someone tell me if I got this geometry question right?

Answer 1

Step-by-step explanation:

Part A.

To get from D to E, we go 5 units right and 2 units up, then we can write the following equation to find the length DE

`5^2+2^2=DE^2`

Solving for DE, we get

`\begin{gathered} DE^2=5^2+2^2 \\ DE^2=25+4 \\ DE^2=29 \\ DE=√(29) \\ DE=5.4 \end{gathered}`

Therefore, DE = 5.4 units

Part B.

To get from D to F, we go 5 units right and 4 units down, so we can write the following equation to find the length of DF

`5^2+4^2=DF^2`

Solving for DF, we get

`\begin{gathered} DF^2=5^2+4^2 \\ DF^2=25+16 \\ DF^2=41 \\ DF=√(41) \\ DF=6.4 \end{gathered}`

Therefore, the length of DF is 6.4 units

Part C.

Then, the perimeter is the sum of all the sides of the triangle, so

Perimeter = DE + DF + FE

Perimeter = 5.4 + 6.4 + 6

Perimeter = 17.8 units