Question

Explain, with a test, why the two triangles in each figure are similar. Find the

unknown lengths.

Answer 1

x = 3, y = 6

Explanation:

In the figure attached,

If ΔADE and ΔABC are similar triangles, their corresponding sides will be in the same ratio.

By this property,

`(AB)/(AD)=(AC)/(AE)=(BC)/(DE)`

`(AB)/(AD)=(AC)/(AE)`

`(AD+BD)/(AD)=(AE+EC)/(AE)`

`(3)/(2)=(x+1.5)/(x)`

3x = 2x + 3

3x - 2x = 3

x = 3

Similarly,
`(AB)/(AD)=(BC)/(DE)`

`(3)/(2)=(y)/(4)`

y =
`(3* 4)/(2)`

y = 6