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# A spotlight on the ceiling is 5 feet from one wall of a room and 10

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
A spotlight on the ceiling is 5 feet from one wall of a room and 10  [#permalink]

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08 Mar 2018, 01:20
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:22) correct 21% (01:18) wrong based on 40 sessions

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A spotlight on the ceiling is 5 feet from one wall of a room and 10 feet from the wall at right angles to it. How many feet is it from the intersection of the two walls?

(A) 15

(B) $$5\sqrt{2}$$

(C) $$5\sqrt{5}$$

(D) $$10\sqrt{2}$$

(E) $$10\sqrt{5}$$

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Posts: 52971
Re: A spotlight on the ceiling is 5 feet from one wall of a room and 10  [#permalink]

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08 Mar 2018, 01:21
Bunuel wrote:
A spotlight on the ceiling is 5 feet from one wall of a room and 10 feet from the wall at right angles to it. How many feet is it from the intersection of the two walls?

(A) 15

(B) $$5\sqrt{2}$$

(C) $$5\sqrt{5}$$

(D) $$10\sqrt{2}$$

(E) $$10\sqrt{5}$$

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Re: A spotlight on the ceiling is 5 feet from one wall of a room and 10  [#permalink]

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08 Mar 2018, 03:01
Attachment:

RtAngledTri.png [ 2.67 KiB | Viewed 525 times ]

Since the spotlight is 5 feet from one wall and 10 feet from another wall,
which is at right angles, the distance from the intersection of the two walls
can be calculated using the Pythogoras theorem

$$x^2 = 5^2 + 10^2$$
$$x^2 = 25 + 100 = 125$$
x = $$\sqrt{125} = 5\sqrt{5}$$

Therefore, the distance between the intersection of the walls and the spotlight is $$5\sqrt{5}$$ (Option C)
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Re: A spotlight on the ceiling is 5 feet from one wall of a room and 10  [#permalink]

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12 Mar 2018, 09:09
Bunuel wrote:
A spotlight on the ceiling is 5 feet from one wall of a room and 10 feet from the wall at right angles to it. How many feet is it from the intersection of the two walls?

(A) 15

(B) $$5\sqrt{2}$$

(C) $$5\sqrt{5}$$

(D) $$10\sqrt{2}$$

(E) $$10\sqrt{5}$$

We can use the Pythagorean theorem, where c is the distance of the spotlight from the intersection of the two walls, and create the following equation:

5^2 + 10^2 = c^2

25 + 100 = c^2

125 = c^2

c = √125 = √25 x √5 = 5√5

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Re: A spotlight on the ceiling is 5 feet from one wall of a room and 10   [#permalink] 12 Mar 2018, 09:09
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