Question

Find the value of x. B X+5 4 D E 2x 3 А x = [?]

Answer 1

Answer:

x = 3

Step-by-step explanation:

Δ BDE and Δ BAC are similar triangles, thus the ratio of corresponding sides are equal, that is

$\frac{BD}{BA}$ = $\frac{BE}{BC}$, substitute values

$\frac{x+5}{3x+5}$ = $\frac{4}{7}$ ( cross- multiply )

4(3x + 5) = 7(x + 5) ← distribute parenthesis on both sides )

12x + 20 = 7x + 35 ( subtract 7x from both sides )

5x + 20 = 35 ( subtract 20 from both sides )

5x = 15 ( divide both sides by 5 )

x = 3