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In the figure, the area of rectangle EFGH is 3 units greater than the

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In the figure, the area of rectangle EFGH is 3 units greater than the  [#permalink]

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New post Updated on: 15 Jul 2019, 04:24
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A
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C
D
E

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Question Stats:

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Originally posted by Bunuel on 09 Oct 2018, 23:41.
Last edited by SajjadAhmad on 15 Jul 2019, 04:24, edited 1 time in total.
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Re: In the figure, the area of rectangle EFGH is 3 units greater than the  [#permalink]

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New post 10 Oct 2018, 00:02
area of rectangle EFGH = 3 + area of rectangle ABCD

(x+a)(x+b) = 3+(x+2)(x+6)

\(x^2\)+x(a+b)+ab = \(x^2\)+8x+15

Given a+b = 8.

Solving gives ab = 15.

C is the answer.
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Re: In the figure, the area of rectangle EFGH is 3 units greater than the  [#permalink]

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New post 10 Oct 2018, 04:57
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Bunuel wrote:
Image
In the figure, the area of rectangle EFGH is 3 units greater than the area of rectangle ABCD. What is the value of ab if a + b = 8?

(A) 9
(B) 12
(C) 15
(D) 18
(E) 21

Attachment:
recs.jpg


\((x+a) * (x+b) = 3 + (x+6)*(x+2)\)

\(x^2 + xb + xa + ab = 3 + x^2 + 2x + 6x + 12\)

\(x^2\) cancel from both side.

take x as a common factor

\(x (a+b) + ab = 3 + x (2+6) + 12\). we are given a+b = 8
\(8x + ab = 15 +8x\)

\(ab = 15\)

Answer choice C
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Re: In the figure, the area of rectangle EFGH is 3 units greater than the  [#permalink]

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New post 10 Oct 2018, 07:47
Bunuel wrote:
Image
In the figure, the area of rectangle EFGH is 3 units greater than the area of rectangle ABCD. What is the value of ab if a + b = 8?

(A) 9
(B) 12
(C) 15
(D) 18
(E) 21

Attachment:
recs.jpg


\((x+a)(x+b) - (x+2)(x+6) = 3\)

Or, \((ab +ax + bx +x^2) - (x^2 +8x + 12) = 3\)

Or, \(ab + x (a + b) - 8x - 12 = 3\)

Or, \(ab + 8x - 8x - 12 = 3\)

Or, \(ab = 15\), Answer must be (C)
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Re: In the figure, the area of rectangle EFGH is 3 units greater than the  [#permalink]

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New post 11 Oct 2018, 01:00
Image

Formula used: Area(Rectangle) = Length * Breadth.
Given: Area(Rectangle EFGH) is 3 units greater than the Area(Rectangle ABCD)

Area(Rectangle ABCD) = \((x+2)(x+6) = x^2 + 8x + 12\) units.
Area(Rectangle EFGH) = \((x+a)(x+b) = x^2 + (a+b)x + ab\) units.

Therefore, the area of the rectangle ABCD is \((x^2 + 8x + 12) + 3 = x^2 + 8x + 15\) and value of ab is 15(Option C)
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Re: In the figure, the area of rectangle EFGH is 3 units greater than the  [#permalink]

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New post 13 Oct 2018, 18:13
Bunuel wrote:
Image
In the figure, the area of rectangle EFGH is 3 units greater than the area of rectangle ABCD. What is the value of ab if a + b = 8?

(A) 9
(B) 12
(C) 15
(D) 18
(E) 21

Attachment:
recs.jpg


We can create the equation:

3 + (x + 2)(x + 6) = (x + a)(x + b)

3 + x^2 + 8x + 12 = x^2 + ax + bx + ab

15 + 8x = ax + bx + ab

15 + 8x = x(a + b) + ab

Since a + b = 8, we have:

15 + 8x = 8x + ab

15 = ab

Answer: C
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Re: In the figure, the area of rectangle EFGH is 3 units greater than the   [#permalink] 13 Oct 2018, 18:13
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