Question

Find the value of x.

B
X+5
4
D
E
2x
3
А
x = [?]

Answer 1

x = 3

Explanation:

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

`(BD)/(BA)` =
`(BE)/(BC)`, substitute values

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