Question : Q is a point in the interior of a rectangle ABCD. If QA = 3 cm, QB = 4 cm and QC = 5 cm, then the length of QD (in cm) is:
Option 1: $3\sqrt2$
Option 2: $5\sqrt2$
Option 3: $\sqrt{34}$
Option 4: $\sqrt{41}$

Question

Question : Q is a point in the interior of a rectangle ABCD. If QA = 3 cm, QB = 4 cm and QC = 5 cm, then the length of QD (in cm) is:

Option 1: $3\sqrt2$

Option 2: $5\sqrt2$

Option 3: $\sqrt{34}$

Option 4: $\sqrt{41}$

Team Careers360 · Accepted Answer

Correct Answer: $3\sqrt2$

Solution :
According to the question, we draw a figure of a rectangle ABCD.
Given that: QA = 3 cm, QB = 4 cm and QC = 5 cm
QD² + QB² = QA² + QC²
⇒ QD² + 16 = 9 + 25
⇒ QD² = 34 – 16 = 18
$ herefore$ QD = $\sqrt{18}= 3\sqrt{2}$ cm
Hence, the correct answer is $3\sqrt{2}$.

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Question : Q is a point in the interior of a rectangle ABCD. If QA = 3 cm, QB = 4 cm and QC = 5 cm, then the length of QD (in cm) is:Option 1: 32Option 2: 52Option 3: 34Option 4: 41

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Question : Q is a point in the interior of a rectangle ABCD. If QA = 3 cm, QB = 4 cm and QC = 5 cm, then the length of QD (in cm) is:
Option 1: $3 \sqrt{2}$
Option 2: $5 \sqrt{2}$
Option 3: $\sqrt{34}$
Option 4: $\sqrt{41}$