Question

Find the ratio of the area of triangle XBY to the area of triangle ABC for the given measurements, if BY = 3, YC = 2

Answer 1

The ratio of the area of triangle XBY to the area of triangle ABC is 9/25.

Pls. see attachment for my image and solutions.

Answer 2

The ratio of the area of triangle XBY to the area of triangle ABC is
`(9)/(25)`

Explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor and the ratio of its areas is equal to the scale factor squared

In this problem

Triangles XBY and ABC are similar, because the corresponding internal angles are congruent

see the attached figure to better understand the problem

step 1

Find the scale factor

Let

z-------> the scale factor

`z=(BY)/(BC)`

we have

`BY=3\ units`

`BC=2+3=5\ units`

substitute

`z=(3)/(5)`

step 2

Find the ratio of the area of triangle XBY to the area of triangle ABC

Remember that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

we have

`z=(3)/(5)` -----> scale factor

so

`z^(2) =((3)/(5))^(2) =(9)/(25)`