## The perimeter of a triangle DEF is 81 units. The length of side DE is twice the length of side EF, and the length of side DF is 4 units

Question

The perimeter of a triangle DEF is 81 units. The length of side DE is twice the length of side EF, and the length of side DF is 4 units less than the length of side DE. Let s represent the length, in units, of side EF. Write an equation that can be used to find s

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2 months 2021-10-14T02:52:17+00:00 2 Answers 0 views 0

5s = 85

Step-by-step explanation:

Perimeter of our triangle = DE + EF + DF = 81 units

We know from the question that

The length of side DE is twice the length of side EF

DE = 2EF

and the length of side DF is 4 units less than the length of side DE

DF = DE – 4

We can replace EF with s in our equations

DE = 2s

And now we can replace DE from the other equation

DF = DE – 4

DF = 2s – 4

If the perimeter of our triangle = DE + EF + DF = 81 units

We will replace the sides with our new values

Perimeter = 2s + s + 2s – 4 = 81

We can put this as our answer, or we can simplify further

Simplify by adding 4 to both sides

2s + s + 2s – 4 + 4 = 81 + 4

Simplify

2s + s + 2s = 85

Simplify

5s = 85

Since the question only asked for an equation, not for us to solve it, we can stop here

(If you wanted to solve for s, just divide both sides by 5)

5s / 5 = 85 / 5

s = 17