Question

Please help with ratios of the area of triangles.....thank you

Answer 1

Part 1) The ratio of the areas of triangle TOS to triangle TQR is
`(4)/(25)`

Part 2) The ratio of the areas of triangle TOS to triangle QOP is
`(4)/(9)`

Explanation:

Part 1) Find the ratio of the areas of triangle TOS to triangle TQR

step 1

Find the scale factor

we know that

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

The scale factor is equal to

TS/TR

substitute the values

6/(6+9)

6/15=2/5

step 2

Find the ratio of the areas of triangle TOS to triangle TQR

we know that

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

so

`((2)/(5))^(2)=(4)/(25)`

Part 2) Find the ratio of the areas of triangle TOS to triangle QOP

step 1

Find the scale factor

we know that

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

The scale factor is equal to

TS/QP

substitute the values

6/9

6/9=2/3

step 2

Find the ratio of the areas of triangle TOS to triangle QOP

we know that

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

so

`((2)/(3))^(2)=(4)/(9)`