The measures of AB= 4, DC= 12, BD= 5, BC= 13.
<u>Step-by-step explanation:</u>
In the figure shown,
The quadrilateral is composed of two right triangles.
From the figure, it can be determined that,
The two right triangles BAD and BDC.
<u>Taking the triangle BAD alone :</u>
- You see three sides of the triangle which are AD, AB and BD.
- From the given data, we already know that AD = 3
<u>To find AB :</u>
It is given in that, AB = AD + 1
Substitute AD = 3,
⇒ AB = 3+1
⇒ AB = 4
<u>To find BD :</u>
Use the Pythagorean triplets (3,4,5)
Therefore, the third side must be 5.
⇒ BD = 5
<u>Taking the triangle BDC alone :</u>
- You see three sides of the triangle which are BD, DC and BC.
- we already found in the previous step that BD = 5
<u>To find DC :</u>
It is given in that, DC = AD × AB
Substitute AD = 3 and AB = 4
⇒ DC = 3 × 4
⇒ DC = 12
<u>To find BC :</u>
Use the Pythagorean triplets (5,12,13)
Therefore, the third side must be 13.
⇒ BC = 12