Question
What is the value of r? Justify each step.
DF=40
DE=3r+6 EF=2r+4
DE+EF = DF a. ___________
3r+6+2r+4=40. b.____________
5r+10=40
5r=30
r=6
DF=40
DE=3r+6 EF=2r+4
DE+EF = DF a. ___________
3r+6+2r+4=40. b.____________
5r+10=40
5r=30
r=6
Answers
Answered by
GPT 3.5
a. The value of DE + EF is equal to DF because they are corresponding sides of a triangle (the sides of a triangle must add up to the length of the third side).
b. By substituting the given lengths into the equation, we get 3r+6+2r+4=40.
c. Simplifying the expression, we combine like terms: 3r+2r+6+4=40, which simplifies to 5r+10=40.
d. We isolate the variable by subtracting 10 from both sides: 5r+10-10=40-10, which simplifies to 5r=30.
e. Finally, we solve for r by dividing both sides by 5: 5r/5=30/5, which simplifies to r=6.
b. By substituting the given lengths into the equation, we get 3r+6+2r+4=40.
c. Simplifying the expression, we combine like terms: 3r+2r+6+4=40, which simplifies to 5r+10=40.
d. We isolate the variable by subtracting 10 from both sides: 5r+10-10=40-10, which simplifies to 5r=30.
e. Finally, we solve for r by dividing both sides by 5: 5r/5=30/5, which simplifies to r=6.
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