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In the figure, the area of rectangle EFGH is 3 units greater
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01 Oct 2018, 13:48
01 Oct 2018, 13:48
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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
Re: In the figure, the area of rectangle EFGH is 3 units greater
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13 Jan 2019, 07:58
13 Jan 2019, 07:58
1
Given that,
Area of rectangle EFGH = Area of rectangle ABCD + 3
i.e. (x + a) ( x + b) = (x + 6) ( x +2) + 3 ( since Area of rectangle = length * breadth)
Multiplying polynomials using FOIL (First, Outer, Inner, Last) and substituting the value of a + b = 8, we get,
ab= 15
Thus, answer is C.
Area of rectangle EFGH = Area of rectangle ABCD + 3
i.e. (x + a) ( x + b) = (x + 6) ( x +2) + 3 ( since Area of rectangle = length * breadth)
Multiplying polynomials using FOIL (First, Outer, Inner, Last) and substituting the value of a + b = 8, we get,
ab= 15
Thus, answer is C.
Re: In the figure, the area of rectangle EFGH is 3 units greater
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13 Jan 2019, 18:42
13 Jan 2019, 18:42
Expert Reply
Carcass wrote:
Attachment:
recs.jpg
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
So Area of EFGH = \((x+a)(x+b)=(x+6)(x+2)+3=x^2+8x+15=(x+5)(x+3)\)..
Thus, a and b are 5 and 3 in no particular order.
ab will always be 3*5=15
C
