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On a perfectly square wall of her office, Christine mounts a whiteboar

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On a perfectly square wall of her office, Christine mounts a whiteboar  [#permalink]

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New post 30 Jan 2018, 00:17
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On a perfectly square wall of her office, Christine mounts a whiteboard that touches the floor and leaves a one-foot border of painted wall space on the other three sides. If that painted wall space around the whiteboard measures 46 square feet, what is the area of the whiteboard, in square feet?

A. 180
B. 210
C. 240
D. 270
E. 300

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Re: On a perfectly square wall of her office, Christine mounts a whiteboar  [#permalink]

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New post 30 Jan 2018, 00:22
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Let s be the side of the square wall. And s^2 is the area of the square.

Now the sides of the whiteboard are (s-1) and (s-2).

Also s^2-((s-1)(s-2))=46

Solving we get s=16

Hence the area of whiteboard = (16-1)(16-2)
=210


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Re: On a perfectly square wall of her office, Christine mounts a whiteboar  [#permalink]

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New post 31 Jan 2018, 17:15
Bunuel wrote:
On a perfectly square wall of her office, Christine mounts a whiteboard that touches the floor and leaves a one-foot border of painted wall space on the other three sides. If that painted wall space around the whiteboard measures 46 square feet, what is the area of the whiteboard, in square feet?

A. 180
B. 210
C. 240
D. 270
E. 300


We can let the length of a side of the wall be x. Thus, the area of the wall is x^2. The height of the whiteboard is (x - 1) because the whiteboard has 1 foot of wall above it. The width of the whiteboard is (x - 2) because there is 1 foot of wall to its left and 1 foot of wall to its right. Thus, the area of the whiteboard is (x - 1)(x - 2). Since the area of the painted wall space around the whiteboard is 46 square feet, we can say:

x^2 - (x - 1)(x - 2) = 46

x^2 - (x^2 - 3x + 2) = 46

3x - 2 = 46

3x = 48

x = 16

Thus, the area of the whiteboard is (16 - 1)(16 - 2) = (15)(14) = 210 square feet.

Answer: B
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Re: On a perfectly square wall of her office, Christine mounts a whiteboar  [#permalink]

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New post 01 Feb 2018, 00:39
Bunuel wrote:
On a perfectly square wall of her office, Christine mounts a whiteboard that touches the floor and leaves a one-foot border of painted wall space on the other three sides. If that painted wall space around the whiteboard measures 46 square feet, what is the area of the whiteboard, in square feet?

A. 180
B. 210
C. 240
D. 270
E. 300


Let l & b be the length & breadth of whiteboard. a - Side of the square.

\(a = l + 2 = b+ 1\)
\((l+2)^2 -l(l+1) = 46\)
\(l = 14, b = 15\)
\(lb = 210.\)
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Re: On a perfectly square wall of her office, Christine mounts a whiteboar   [#permalink] 01 Feb 2018, 00:39
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