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# Area of a rectangle X is 24cm^2 greater than the area of rectangle Y.

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Manager
Joined: 07 Jun 2018
Posts: 51
Location: United States
Area of a rectangle X is 24cm^2 greater than the area of rectangle Y.  [#permalink]

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20 Dec 2018, 13:45
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Difficulty:

5% (low)

Question Stats:

95% (02:30) correct 5% (02:53) wrong based on 34 sessions

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Area of a rectangle X is 24cm^2 greater than the area of rectangle Y. The width of the rectangle X is 4 cm greater than the width of rectangle Y, and the length of rectangle X is 2 cm less than the length of rectangle Y. If the perimeter of rectangle Y is 40 cm, which of the following is the area of rectangle Y?

72 cm^2
84 cm^2
96 cm^2
108 cm^2
112 cm^2
Intern
Joined: 24 Mar 2018
Posts: 45
Location: Egypt
Concentration: Entrepreneurship, General Management
Schools: Stanford '22, HEC, Cass, EDHEC
WE: Analyst (Computer Software)
Area of a rectangle X is 24cm^2 greater than the area of rectangle Y.  [#permalink]

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20 Dec 2018, 22:24
I had to redo it again as its steps were unfamiliar, nice question BTW.

Jazzmin wrote:
Area of a rectangle X is 24cm^2 greater than the area of rectangle Y. The width of the rectangle X is 4 cm greater than the width of rectangle Y, and the length of rectangle X is 2 cm less than the length of rectangle Y. If the perimeter of rectangle Y is 40 cm, which of the following is the area of rectangle Y?

72 cm^2
84 cm^2
96 cm^2
108 cm^2
112 cm^2
Senior Manager
Joined: 15 Feb 2018
Posts: 367
Re: Area of a rectangle X is 24cm^2 greater than the area of rectangle Y.  [#permalink]

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26 Jan 2019, 22:41
Someone please post a step-by-step solution.

Jazzmin what is the question source?
Director
Joined: 09 Mar 2018
Posts: 994
Location: India
Area of a rectangle X is 24cm^2 greater than the area of rectangle Y.  [#permalink]

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26 Jan 2019, 23:07
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philipssonicare wrote:
Someone please post a step-by-step solution.

Jazzmin what is the question source?

philipssonicare, i followed this approach,

I thought of solving this with some other approach, but landed up using a fool proof one

a1 and b1 are length and breadth of x respectively

a2 and b2 are length and breadth of y respectively

a1 * b1 = 24 + a2 *b2 (given)

b1 = 4 + b2
l1 = l2 - 2

put l1 and b1 back in given

l2-2 * 4+ b2 = 24 + a2 b2

Just cross multiply LHS to get

4* l2 - 2 * b2 = 32
2 * l2 -16 = b2

Now its given perimeter of Y is 40

2 ( l2 + b2) = 40

l2 + 2 * l2 -16 = 20
3 * l2 = 36
l2 = 12

Use value of l2 in b2

b2 = 24 - 16 = 8

Area of Y = l2 * b2
= 12 * 8
= 96 unit^2

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Area of a rectangle X is 24cm^2 greater than the area of rectangle Y.   [#permalink] 26 Jan 2019, 23:07
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