Question

Triangle ABE is similar to triangle ACD. AB=2 , AC= y-2 , BE=5, and CD=y-3. Find y.

Answer 1

y =
`(4)/(3)`

Explanation:

Given that the triangles are similar then the ratios of corresponding sides are equal, that is

`(AB)/(AC)` =
`(BE)/(CD)`, substituting values

`(2)/(y-2)` =
`(5)/(y-3)` ( cross- multiply )

5(y - 2) = 2(y - 3) ← distribute both sides

5y - 10 = 2y - 6 ( subtract 2y from both sides )

3y - 10 = - 6 ( add 10 to both sides )

3y = 4 ( divide both sides by 3 )

y =
`(4)/(3)`