Question

In the diagram, line XY is || to line AC. Use the diagram to answer the following.

If BX= 4, BA=5, and BY = 6, what is BC?

Answer 1

Given
`\(BX = 4\),`
`\(BA = 5\)` , and
`\(BY = 6\)` in similar triangles
`\(BXY\)` and
`\(BAC\)`, using the ratio of corresponding sides,
`\(BC\)` equals 7.5 units.

Sure, let's solve step by step using the properties of similar triangles.

Given:

`\(BX = 4\)`,

`\(BA = 5\)`,

`\(BY = 6\).`

We have two parallel lines
`(\(XY\) )` and
`(\(AC\))` intersected by transversal (AB), which creates similar triangles (BXY) and (BAC).

The ratio of corresponding sides in similar triangles is equal:

`\(\frac{{BX}}{{BA}}` =
`\frac{{BY}}{{BC}}\)`

Substituting the given values:

`\((4)/(5)` =
`(6)/(BC)\)`

To solve for
`\(BC\),` cross multiply:

`\(4 * BC = 5 * 6\)`

`\(4BC = 30\)`

Divide both sides by 4 to isolate
`\(BC\)`:

`\(BC = (30)/(4)\)`

Simplify:

`\(BC = 7.5\)`

Therefore,
`\(BC = 7.5\)`.