Question

AE = 3x - 2 and EC = 2x + 3 then DB =

#5

Answer 1

DB = 26

Explanation:

Remember:

• AE ≅ EC
• AC ≅ DB

☆The equation in finding the value of x would be 3x - 2 = 2x + 3.

☆Let's solve the equation.

`\: \: \: \: \: \: \: \: \: 3x - 2 = 2x + 3 \\ ( - 2x \: \: \: \ = - 2x)/(x - 2 = 3) \\ ( \: \: \: \: \: + 2 = + 2)/(x = 5)`

☆Now that we found the value of x, we are going to plug in for AE and EC.

`AE ; \\ 3x - 2 \\ 3(5) - 2 \\ 15 - 2 \\ 13 \\ \\ \\ \\ and \\ \\ \\ \\ \\ EC; \\ 2x + 3 \\ 2(5) + 3 \\ 10 + 3 \\ 13`

☆AE and EC each measure 13. To find the length of AC, you will have to add AE and EC.
`13 + 13 = 26`

The length of AC is 26. And since we know that AC is congruent (equal) to DB, meaning they measure the same. DB length is also 26.