Question

5

The diagram shows two right-angled triangles. OAB
and OCD
Work out the length of BD. I
7 cm
4 cm
14 cm

Answer 1

The possible length of the segment BD is 10.5

How to determine the possible length of the segment BD

From the question, we have the following parameters that can be used in our computation:

The similar triangles

Using the proportional equation of similar triangles, we have

4/14 = 7/(14 + BD)

So, we have

(14 + BD) * 4 = 7 * 14

(14 + BD) * 4 = 98

Divide

14 + BD = 24.5

This gives

BD = 10.5

Hence. the possible length of the segment BD is 10.5

Answer 2

Given:

The diagram shows two right-angled triangles OAB and OCD.

To find:

The length of BD.

Solution:

Let the length of BD is x.

In triangle OAB and OCD,

`\angle AOB\cong \angle COD` (Common angle)

`\angle ABO\cong \angle CDO` (Right angle)

`\Delta OAB\sim OCD` (By AA property of similarity)

We know that, the corresponding sides of similar triangles are proportional. So,

`(AB)/(CD)=(OB)/(OD)`

`(4)/(7)=(14)/(14+x)`

`4(14+x)=14(7)`

`56+4x=98`

Subtracting 56 from both sides, we get

`4x=98-56`

`4x=42`

`x=(42)/(4)`

`x=10.5`

Therefore, the length of BD is 10.5 cm.