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# A rectangle is formed by increasing two opposite sides of a square of

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Joined: 02 Sep 2009
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A rectangle is formed by increasing two opposite sides of a square of  [#permalink]

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26 Jun 2018, 04:26
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Difficulty:

15% (low)

Question Stats:

90% (01:08) correct 10% (01:28) wrong based on 38 sessions

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A rectangle is formed by increasing two opposite sides of a square of side length x by y units, and decreasing the two remaining sides of the square by y units. What is the area of the rectangle?

A. $$4x$$

B. $$4x - 2y$$

C. $$x^2 - 2y$$

D. $$x^2 + 2y$$

E. $$x^2 - y^2$$

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Posts: 2323
Re: A rectangle is formed by increasing two opposite sides of a square of  [#permalink]

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26 Jun 2018, 04:31

Solution

Given:
• A rectangle is formed by increasing two opposite sides of a square of side length x by y units, and decreasing the two remaining sides of the square by y units

To find:
• The area of the rectangle

Approach and Working:
• The length of the rectangle = x + y
• The breadth of the rectangle = x – y
• Therefore, the area of the rectangle = (x + y) (x – y) = $$x^2 – y^2$$

Hence, the correct answer is option E.

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Re: A rectangle is formed by increasing two opposite sides of a square of  [#permalink]

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26 Jun 2018, 08:17
Bunuel wrote:
A rectangle is formed by increasing two opposite sides of a square of side length x by y units, and decreasing the two remaining sides of the square by y units. What is the area of the rectangle?

A. $$4x$$

B. $$4x - 2y$$

C. $$x^2 - 2y$$

D. $$x^2 + 2y$$

E. $$x^2 - y^2$$

The 2 sides of the Rectangle are $$(x + y)$$ and $$(x - y)$$, thus area of the rectangle is $$x^2 - y^2$$, answer must be (E)
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Re: A rectangle is formed by increasing two opposite sides of a square of  [#permalink]

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27 Jun 2018, 17:12
Bunuel wrote:
A rectangle is formed by increasing two opposite sides of a square of side length x by y units, and decreasing the two remaining sides of the square by y units. What is the area of the rectangle?

A. $$4x$$

B. $$4x - 2y$$

C. $$x^2 - 2y$$

D. $$x^2 + 2y$$

E. $$x^2 - y^2$$

The area of the rectangle is (x + y)(x - y) = x^2 - y^2 square units.

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Re: A rectangle is formed by increasing two opposite sides of a square of &nbs [#permalink] 27 Jun 2018, 17:12
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