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If Triangle ABC~ triangle DEC, find the value of x and the scale factor from DEC to ABC

If Triangle ABC~ triangle DEC, find the value of x and the scale factor from DEC to-example-1
User Jason Nam
by
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2 Answers

19 votes
19 votes

Answer:

see explanation

Explanation:

The scale factor is the ratio of corresponding sides, image to original, that is

scale factor =
(AC)/(DC) =
(25)/(20) =
(5)/(4)

Then


(AB)/(DE) =
(3x-2)/(2x) =
(5)/(4) ( cross- multiply )

4(3x - 2) = 10x

12x - 8 = 10x ( subtract 10x from both sides )

2x - 8 = 0 ( add 8 to both sides )

2x = 8 ( divide both sides by 2 )

x = 4

User Danielschnoll
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3.0k points
13 votes
13 votes

The scale factor from
\(\triangle DEC\) to \(\triangle ABC\) is 8:25, and the value of x is 4.

To find the value of x and the scale factor from
\(\triangle DEC\) to \(\triangle ABC\), we can use the fact that corresponding sides of congruent triangles are in proportion.

Let AB = 3x - 2 and DE = 2x.

According to the proportionality of corresponding sides:


\[(AB)/(DE) = (AC)/(CD)\]

Substitute the given values:


\[(3x - 2)/(2x) = (25)/(20)\]

Now, solve for x:


\[20(3x - 2) = 25(2x)\]

Distribute and simplify:


\[60x - 40 = 50x\]

Subtract 50x from both sides:


\[10x - 40 = 0\]

Add 40 to both sides:


\[10x = 40\]

Divide by 10:


\[x = 4\]

So, x = 4.

Now, to find the scale factor, substitute x back into the expression for DE:


\[DE = 2x = 2 * 4 = 8\]

The scale factor from
\(\triangle DEC\) to \(\triangle ABC\) is 8:25, and the value of x is 4.

User DrLazer
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2.6k points