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# What is the area of a rectangle if its width is half its length?

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Math Expert
Joined: 02 Sep 2009
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What is the area of a rectangle if its width is half its length?  [#permalink]

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24 Aug 2018, 04:20
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Difficulty:

15% (low)

Question Stats:

81% (00:53) correct 19% (00:52) wrong based on 43 sessions

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What is the area of a rectangle if its width is half its length?

(1) The perimeter of the rectangle is 30.
(2) The diagonal of the rectangle has length $$5\sqrt{5}$$.

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Re: What is the area of a rectangle if its width is half its length?  [#permalink]

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24 Aug 2018, 04:32
Bunuel wrote:
What is the area of a rectangle if its width is half its length?

(1) The perimeter of the rectangle is 30.
(2) The diagonal of the rectangle has length $$5\sqrt{5}$$.
Simplified question stem : what is the length of the rectangular

1) don't calculate. It gives us the length
Sufficient

2) gives us the length
Sufficient

D

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Re: What is the area of a rectangle if its width is half its length?  [#permalink]

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24 Aug 2018, 04:47
Bunuel wrote:
What is the area of a rectangle if its width is half its length?

(1) The perimeter of the rectangle is 30.
(2) The diagonal of the rectangle has length $$5\sqrt{5}$$.

Question stem:-What is the area of a rectangle?

Required data:-
a) Length and
b) width

Given:- Relationship b/w length and width

St1:- The perimeter of the rectangle is 30.
Since relationship b/w L and W is known, hence we can determine the values of L and W.
So, area can be determined.
Sufficient.

St2:- The diagonal of the rectangle has length $$5\sqrt{5}$$
Measure of the three sides of the right angled triangel formed by the diagonal: L, L/2 and $$5\sqrt{5}$$.
We can determine L using pythagoras formula. Hence, w can be determined.
Sufficient to determine area.

Ans. (D)
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What is the area of a rectangle if its width is half its length?  [#permalink]

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24 Aug 2018, 05:34
Bunuel wrote:
What is the area of a rectangle if its width is half its length?

(1) The perimeter of the rectangle is 30.
(2) The diagonal of the rectangle has length $$5\sqrt{5}$$.

Length = 2x

Width = x

Statement 1: perimeter = 30

2(2x + x ) = 30

x = 5.

2x = 10

Area: 5*10 = 50

Statement 2: Diagonal = 5$$\sqrt{5}$$

As it's a rectangle, its diagonal is basically the hypotenuse of right angle.

So, we have our chance to apply Pythagorean Theorem.

$$(2x)^2$$ + $$x^2$$= $$(5\sqrt{5})^2$$
Solving the equation we will get the value of x.

So, it's possible to determine the value of the area of rectangle.

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Re: What is the area of a rectangle if its width is half its length?  [#permalink]

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24 Aug 2018, 09:21

Solution

Given:
• Width of rectangle = 1/2 * length of rectangle

To find:
• Area of the rectangle

Approach and Working:
• Area of rectangle = l * b, and we know that, l = 2b
• Thus, we can find the area, if we know the value of l or b

Analysing Statement 1
• Perimeter = 30, implies, 2(l+b) = 30
• l+b = 15, implies, 3b = 15
• Thus, b = 5
• Hence, we can find the area of the rectangle
Therefore, Statement 1 alone is sufficient to answer this question

Analysing Statement 2
• Diagonal = 5√5, implies, $$√ (l^2 + b^2) = 5√5$$
• Squaring on both sides gives, $$(l^2 + b^2) = 25 * 5$$
• Implies, $$5b^2 = 125$$, which gives the value of b as 5
Therefore, Statement 2 alone is sufficient to answer this question.

Hence, the correct answer is option D.

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What is the area of a rectangle if its width is half its length?  [#permalink]

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25 Aug 2018, 05:16
Let length of rectangle= 2x

.............Width...........= x

Area= 2$$x^2$$

1) Perimeter= 2(L+B)= 2(2x+x)= 30. Value of x can be found. [Suff]

2) $$x^2$$+4$$x^2$$= $$(5\sqrt{5})^2$$. Value of x can be found. [Suff]

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What is the area of a rectangle if its width is half its length? &nbs [#permalink] 25 Aug 2018, 05:16
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