Question

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

Answer 1

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

Answer 2

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.