Question

2. ABCD is a quadrilateral composed of two right triangles where AD = 3,

AB = AD + 1, and DC = AD *AB.
a. Find AB, DC, BD, and BC.

Answer 1

The measures of AB= 4, DC= 12, BD= 5, BC= 13.

Explanation:

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.

Taking the triangle BAD alone :

• You see three sides of the triangle which are AD, AB and BD.
• From the given data, we already know that AD = 3

To find AB :

It is given in that, AB = AD + 1

Substitute AD = 3,

⇒ AB = 3+1

⇒ AB = 4

To find BD :

Use the Pythagorean triplets (3,4,5)

Therefore, the third side must be 5.

⇒ BD = 5

Taking the triangle BDC alone :

• You see three sides of the triangle which are BD, DC and BC.
• we already found in the previous step that BD = 5

To find DC :

It is given in that, DC = AD × AB

Substitute AD = 3 and AB = 4

⇒ DC = 3 × 4

⇒ DC = 12

To find BC :

Use the Pythagorean triplets (5,12,13)

Therefore, the third side must be 13.

⇒ BC = 12