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# Which expression represents the length of PQ in terms of a, b, and c?

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Math Expert
Joined: 02 Sep 2009
Posts: 50610
Which expression represents the length of PQ in terms of a, b, and c?  [#permalink]

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11 Sep 2018, 23:57
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Difficulty:

(N/A)

Question Stats:

45% (00:44) correct 55% (01:10) wrong based on 11 sessions

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Which expression represents the length of PQ in terms of a, b, and c?

A. $$\sqrt{a^2 + ac}$$

B. $$\sqrt{a^2 + 2ac - b^2}$$

C. $$\sqrt{a^2 - b^2}$$

D. $$a + c - \sqrt{b^2 + c^2}$$

E. $$\sqrt{b^2 - ac}$$

Attachment:

image027.jpg [ 2.5 KiB | Viewed 267 times ]

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Re: Which expression represents the length of PQ in terms of a, b, and c?  [#permalink]

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12 Sep 2018, 00:47
Bunuel wrote:

Which expression represents the length of PQ in terms of a, b, and c?

A. $$\sqrt{a^2 + ac}$$

B. $$\sqrt{a^2 + 2ac - b^2}$$

C. $$\sqrt{a^2 - b^2}$$

D. $$a + c - \sqrt{b^2 + c^2}$$

E. $$\sqrt{b^2 - ac}$$

Attachment:
image027.jpg

PQR is a right angled triangle (Angle made by semi-circle is 90 degree)

$$QR^2=b^2+c^2$$

$$PQ=\sqrt{PR^2-QR^2}$$=$$\sqrt{(a+c)^2-(b^2+c^2)}=\sqrt{a^2+c^ 2+2ac-b^2-c^2}$$=$$\sqrt{a^2 + 2ac - b^2}$$

Ans. (B)
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Re: Which expression represents the length of PQ in terms of a, b, and c? &nbs [#permalink] 12 Sep 2018, 00:47
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# Which expression represents the length of PQ in terms of a, b, and c?

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