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

Question

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} .

sumit411 · Answer

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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PKN · Answer

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)

KSBGC · Answer

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.

The best answer is D.

EgmatQuantExpert · Answer

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.

Answer: D

https://e-gmat.com/blogs/wp-content/uploads/2016/12/Geometry-Ability-Quiz-4-e1480581478957.png

varun4s · Answer

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

Answer: D.

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

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