Question

ANSWER QUICKLY PLEASE!!

Answer 1

The lines on each of the sides of the triangle indicate that all of the sides are the same (it is an equilateral triangle)

This means that side EF is equal to side DF.

Therefore:

$\frac{2}{5} a -15$ = $\frac{1}{5} a - 5$

All we do now is solve the equation, like so:

$\frac{2}{5} a -15$ = $\frac{1}{5} a - 5$

$\frac{2}{5} a$ = $\frac{1}{5} a - 10$ (add 15 to both sides to get  $\frac{2}{5} a$ by itself)

$\frac{1}{5} a$ = 10 ( subtract $\frac{1}{5} a$ from both sides to get all the a's on one side)

a = 50  (times both sides by 5, to get what just a is equal to)

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Now that we know what a is equal to (50) we can find the value of a side by substituting it into one of the expressions on the image:

$\frac{1}{5} a - 5$

= $\frac{1}{5} 50- 5$     (replace a with 50)

= 10 - 5         ( 50 divided by 5, then multiplied by 1 is 10)

= 5

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Answer

DE = 5

(Note: if you have any other questions, don't hesitate to ask)