A 2 min read

Solution

Given

In this question, we are given

• The diagram of the quadrilateral ABCD
• Length of AD = 1, DC = 3 and CB = 4
• Angle BAD = angle DCB = 90°

 

To Find

We need to determine

• The length of AB

 

Approach & Working

In the given figure, if we add the points B and D, we get two right-angle triangles ABD and CBD.

Now, in triangle BCD, angle BCD = 90°

• Therefore, BD² = BC² + CD² = 4² + 3² = 16 + 9 = 25 = 5²
• Hence, BD = 5

Similarly, in triangle BAD, angle BAD = 90°

• Hence, BD² = BA² + AD²

Or, BA² = BD² – AD² = 5² – 1² = 25 – 1 = 24 = 4 * 6

• Therefore, BA = √(4 * 6) = 2√6

Hence, the correct answer is option C.

 

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