A certain rectangular window is twice as long as it is wide.

Ya its quite easy....

twice as long as it is wide means : l=2w

Given p=10
2(l+w)=10
l+w=5
2w+w=5
w=5/3
and l = 10/3

If u feel difficult in understanding "twice as long as it is wide", since length should be always greater than width and here it is twice l=2w

Width \(=\) \(x\)
Length\(=\) \(2x\)
Perimeter \(= x+x+2x+2x = 6X\)
\(6x = 10\)
\(x= \frac{5}{3}\)

Therefore, dimensions are:
Width \(= \frac{5}{3}\)
Length \(= 2*\frac{5}{3} = \frac{10}{3}\)


B all the way

We can eliminate C,D,E as not giving 10 feeet as perimeter. In choice A, 3/2=1.5 and 7/2=3.5 so it is not double difference. The answer is B

The dimesnsions of the box are:
w = w
l = 2w

Perimeter:
2w + 2(2w) = 10
2w + 4w = 10
6w = 10
w = 10 / 6
w = 5 / 3

l = 2w
l = 2 (5/3)
l = 10 / 3

So. the dimensions are 5/3 and 10/3, ANS B

HI All,

Many Test Takers would approach this with a combination of algebra and geometry rules, which is fine - the math is easy enough to do. On Test Day though, you have 2 goals when dealing with a question:

1) Get it correct, if possible.
2) Answer it in the fastest way possible.

Since the answer choices ARE numbers, and the prompt describes some rather specific facts, you can use the answers to your advantage and TEST THE ANSWERS.

We're told 2 things about a rectangle:
1) It's length is TWICE it's width.
2) It's perimeter is 10

We're asked for the dimensions of the rectangle.

Looking at the answer choices, there are some really easy answers to knock out....

Answer C: 2 by 4......this perimeter would = 12, not 10. ELIMINATE C.
Answer D: 3 by 6......this perimeter would = 18, not 10. ELIMINATE D.
Answer E: 10/3 by 20/3......this perimeter would be > 18, not 10. ELIMINATE E.

With the remaining 2 answers, only 1 of them has a length that is TWICE the width....

Answer A: 3/2 and 7/2.....7/2 is NOT TWICE 3/2. Eliminate A.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

We set up the dimensions of the rectangular window as w = width and l = length.

We are given that the rectangular window is twice as long as it is wide. Thus we can say:

l = 2w

We also know that the perimeter is 10 feet, so we can say:

2l + 2w = 10

We can now substitute in 2w for l and we have:

2 x 2w + 2w = 10

4w + 2w = 10

6w = 10

w = 10/6 = 5/3

Because we know that the length is twice the width, we know that the length is:

2 x 5/3 = 10/3

Answer B.

Take width as x, length is 2x. Perimeter = x+2x+x+2x = 6x = 10; x=5/3

Hence length is 10/3 and width is 5/3
Answer is B.

We COULD use algebra to solve this question.
However, it's probably faster to just test the answer choices

The answer choices give us the length and width of the rectangle.
So, the sum of two values will equal HALF the perimeter of the rectangle.
Since we want a perimeter of 10, the correct answer choice will have a sum of 5 ( HALF the perimeter)

(A) 3/2 by 7/2
3/2 + 7/2 = 10/2 = 5
Yay!!!
Hold on!
The question tells us the length is TWICE the width, yet 7/2 is NOT twice 3/2
ELIMINATE A

(B) 5/3 by 10/3
5/3 + 10/3 = 15/3 = 5. GREAT!
Also, 10/3 IS TWICE 5/3

Answer: B

Cheers,
Brent

Approach #2: Algebra

Let x = the width of the rectangle
So, 2x = the length of the rectangle

If the perimeter is 10, we can write: x + x + 2x + 2x = 10
Simplify: 6x = 10
Solve: x = 10/6 = 5/3
So, the width (x) is 5/3
And the length (2x) is 10/3

Answer: B

Cheers,
Brent

given l=2w
and 2*(l+w)= 10
l+w= 5
and w= 5/3 and l= 10/3
IMO B

ALTERNATE APPROACH , CHECKING THE ANSWER OPTIONS

(A) 3/2 & 7/2 , ie 1.5 & 3.5 , Thus perimeter will be 10 but length is not 2 times width , hence rejected.
(B) (5/3 + 10/3)*2 = 10 , Further perimeter is 10 ( Possible)
(C) (2 + 4 )*2 = 12 , Not possible
(D) (3+6)*2 = 18, Not possible
(E) (10/3 + 20/3)*2 = 20 , Perimeter not possible.

Hence, Answer must be (B)

Given: A certain rectangular window is twice as long as it is wide.

Asked: If its perimeter is 10 feet, then its dimensions in feet are

l =2w
2(l+w) = 10
2*3w = 10
w = 5/3
l = 10/3
Rectangular window's dimensions in feet are 5/3 and 10/3.


IMO B

Let's denote the width of the rectangular window as 'w'. Since the window is twice as long as it is wide, the length can be expressed as '2w'.

The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)

We are given that the perimeter of the window is 10 feet, so we can set up the following equation:
2(2w + w) = 10

Simplifying the equation, we have:
2(3w) = 10
6w = 10
w = 10/6 = 5/3

Therefore, the width of the window is 5/3 feet.

To find the length, we can substitute the value of the width into the equation for the length:
Length = 2w = 2 * (5/3) = 10/3

Therefore, the length of the window is 10/3 feet.

Hence, the dimensions of the rectangular window are 5/3 by 10/3 feet, which corresponds to option (B).