The size of a television screen is given as the length of

Question

The size of a television screen is given as the length of the screen's diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 19-inch screen?

A. 2
B. 4
C. 16
D. 38
E. 40

A. 2
B. 4
C. 16
D. 38
E. 40

Bunuel · Accepted Answer

Given:  d_1=21  and  d_2=19 .

area_{square}=\frac{d^2}{2} ;

area_1-area_2=\frac{(d_1)^2}{2}-\frac{(d_2)^2}{2}=\frac{21^2-19^2}{2}=\frac{(21-19)(21+19)}{2}=\frac{2*40}{2}=40

Answer: E.

BrentGMATPrepNow · Answer

Let x be the length (and width) of the square screen with diagonal 21
The area of the large screen will be x²

Let y be the length (and width) of the square screen with diagonal 19
The area of the small screen will be y²

Our goal is to find the value of x² - y²

Large TV: If we examine the right triangle created by 2 sides (both with length x) and the diagonal, we can apply the Pythagorean Theorem to get x² + x² = 21²
When we simplify this, we get 2x² = 441, which means x² = 441/2

Small TV: If we examine the right triangle created by 2 sides (both with length y) and the diagonal, we can apply the Pythagorean Theorem to get y² + y² = 19²
When we simplify this, we get 2y² = 361, which means y² = 361/2

We can now find the value of x² - y²
We get x² - y² = 441/2 - 361/2 = 80/2 = 40

Answer: E

Cheers, 
Brent

medanova · Answer

the diagonal of a square is always  side*\sqrt{2} 
and the side of a square is vice versa always  \frac{diagonal}{\sqrt{2}}

Therefore:
area of the bigger one is  (\frac{21}{\sqrt{2}})^2 
area of the smaller one is  (\frac{19}{\sqrt{2}})^2 
and the difference is = 40

manavecplan · Answer

Just to refresh my understanding, how is the  area_{square}=\frac{d^2}{2}

The side x side is simple enough. Given that a square is essentially 2 isoceles triangles, I was going with 21= x\sqrt{2}

That's where I got stuck. But I still don't get your formula...

Bunuel · Answer

The area of a square is  side^2 , but since here the length of the diagonal is given, then it's better to use another formula  area_{square}=\frac{diagonal^2}{2} .

WholeLottaLove · Answer

The size of a television screen is given as the length of the screen's diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 19-inch screen?

A. 2
B. 4
C. 16
D. 38
E. 40

A. 2
B. 4
C. 16
D. 38
E. 40

We're dealing with squares here. When you take the diagonal of a square it creates two isosceles triangles with a ratio of x: x: x√2. Because the hypotenuse is 21 inches it is equal to x√2. To find the length of the legs, we set 21 = x√2. x = 21/√2
To find the area we square 21/√2 which equals 441/2. Similarly, for the 19 inch screen we follow the same steps. We find that the legs of the triangle (or the sides of the square screen) are 19/√2 inches. To find the area we square this to get 361/2. Finally, subtract 361/2 from 441/2 to get 80/2 = 40.

E

ScottTargetTestPrep · Answer

Let’s determine the side of the square 21-inch screen (i.e., the diagonal of the screen is 21 inches). Recall that the diagonal of a square is equal to side√2.

21 = side√2

21/√2 = side

Since area is side^2, the area of the 21-inch screen is (21/√2)^2 = 441/2.

Let’s determine the side of the square 19-inch screen:

19 = side√2

19/√2 = side

The area of the 19-inch screen is (19/√2)^2 = 361/2.

Thus, the difference is 441/2 - 361/2 = 80/2 = 40.

Alternate solution:

We are given two square TV screens with diagonals 21 and 19, respectively. We have to determine the difference between the areas of the screens. Recall that the area of a square, given its diagonal d, is A = d^2/2. Thus, the area of the 21-inch screen is 21^2/2 = 441/2 and the area of the 19-inch screen is 19^2/2 = 361/2. Therefore, the difference in areas is 441/2 - 361/2 = 80/2 = 40.

Answer: E

Luckisnoexcuse · Answer

area of a square 21-inch screen = (21/\sqrt{2})^2 = 441/2
area of a square 19-inch screen = (19/\sqrt{2})^2 = 361/2

Diff = 80/2 = 40
E

generis · Answer

If the size of a square television screen is given by its diagonal, we need side lengths to calculate area.

The relationship between the a square's side and its diagonal, d, is given by

s\sqrt{2} = d 
 s = \frac{d}{\sqrt{2}}

The side of the 21-inch size television (d = 21), therefore, is

\frac{21}{\sqrt{2}} . Square that to find area:

(\frac{21}{\sqrt{2}}  *  \frac{21}{\sqrt{2}})  =  \frac{21*21}{2}  =  \frac{441}{2}

The side of the 19-inch size television (d = 19) is

\frac{19}{\sqrt{2}} . Square that to find area:

(\frac{19}{\sqrt{2}}  *  \frac{19}{\sqrt{2}})  =  \frac{19*19}{2}  =  \frac{361}{2}

Difference in area between larger and smaller, in square inches:

(\frac{441}{2} - \frac{361}{2}) =\frac{80}{2} = 40

Answer E

dylanl1218 · Answer

I love this question because it's quite literally the definition of the difference of two square (i.e. X^2 - Y^2 = (X+Y)(X-Y).

So start off remember that if you take the diagonal of a square then you get two triangles each with side ratios of X, X and Xsqrt(2). So this means that the sides of each of the TVs can be determined by the equation of Side of Square X Sqrt(2) = Diagonal.

Side of first TV = 21/Sqrt(2)
Side of second TV = 21/Sqrt(2)

Thus we want to take the difference of the AREA of the first and second TV. So (21/sqrt(2))^2 - (19/sqrt(2))^2, which can be solved further as (21^2 - 19^2)/2, so (21+19)(21-19)/2 = 40(2)/2 so 40 which is answer choice E is the answer.

Panahtistrats5 · Answer

Kinda late to the party, but how do we know that the screen is a square?

I don't see many perfect square screens around to be honest.

Is this question ancient OG, like pre 2005 when TVs were huge square bricks?

That would explain it

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

The size of a television screen is given as the length of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

The size of a television screen is given as the length of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards