Question

Find all the missing measurement​

Answer 1

Given:

`\Delta CAP\sim \Delta DAY`

To find:

The value of FD.

Solution:

We have,
`\Delta CAP\sim \Delta DAY`. So, the corresponding angles are congruent.

`\angle CAP\cong \angle DAY`

`\angle ACL\cong \angle AD F` (Given in the figure)

Two angles are congruent. So,

`\Delta CAL\sim \Delta DA F`

Corresponding sides of similar triangles are proportional. So,

`(CA)/(DA)=(LC)/(FD)`

Substituting the given values from the figure, we get

`(35)/(21)=(25)/(FD)`

`(5)/(3)=(25)/(FD)`

On cross multiplication, we get

`5* FD=3* 25`

`5FD=75`

Divide both sides by 5.

`FD=(75)/(5)`

`FD=15`

Therefore, the measure of FD is 15 units.