Question

In ΔPQR, m∠Q = 90 and PQ = QR. QM ⊥ PR, M ∈ PR. If QM = 2, PQ = ......D
(a) 4
(b) 2√2
(c) 8
(d) 2

Answer 1

Acc to the question, in ΔPQR, m∠Q = 90 and PQ = QR. QM ⊥ PR, M ∈ PR.

Let us assume PQ = QR = x.

or, x² + x² = PR²

or, PR = x√2.

Now, PM = MR = x/√2.

or, PM² + QM² = PQ².

or, (x/√2)² + 2² = x²

or, x²/2 + 4 = x².

or, x² - x²/2 = 4.

or, x²/2 = 4.

oe, x² = 8.

or, x = √8 = 2√2.

Therefore, PQ = 2√2.

Answer 2

1/p² = 1/a² + 1/b²

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Here ,

PQ = QR

QM = 2

1/PQ² + 1/QR² = 1/MQ²

1/PQ² + 1/PQ² = 1/2²

2/PQ² = 1/4

PQ² = 8

PQ = √8

PQ = √ 2 × 2 × 2

PQ = 2√2

Option ( b ) correct

I hope this helps you.

: )