Question

A

X
Find the value of x.
D
X+2
x = [?]
B
3
E.
2
C
Enter

Answer 1

x = 4

Explanation:

Similarity of triangle ABC and DBE:

• Triangles ABC and DBE are similar by the Angle-Angle (AA) similarity rule.
• Since DE is parallel to AC, we have two sets of corresponding angles, which are equal.
• Angles BDE and BAC are the first set of corresponding angles, while angles BED and BCA are the other set.

• In similar triangles, the sides are also similar and proportional.
• This means that sides BD and BA are similar and proportional (BD / BA), while sides BE and BC are similar and proportional (BE / BC).

Now we can use these proportions to find x:

BD / BA = BE / BC

(x + 2) / (x + 2 + x) = 3 / (3 + 2)

Combining like terms gives us:

(x + 2) / 2x + 2 = 3 / 5

Cross multiplying gives us:

3(2x + 2) = 5(x + 2)

6x + 6 = 5x + 10

Subtracting 6 from both sides gives us:

(6x + 6 = 5x + 10) - 6

6x = 5x + 4

Subtracting 5x from both sides gives us:

(6x = 5x + 4) - 5x

x = 4

Thus, x = 4

Check the validity of the answer:

We can check our answer by plugging in 4 for x and seeing if we get 3/5 on both sides:

(4 + 2) / (4 + 2 + 4) = 3/5

6 / 10 = 3/5

3/5 = 3/5

Thus, our answer is correct.