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

Question

The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television?

A. 106.75
B. 213.5
C. 427
D. 729
E. 1,156

A. 106.75
B. 213.5
C. 427
D. 729
E. 1,156

paidlukkha · Answer

34^2-27^2 = 427

C

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ShravyaAlladi · Answer

Diagonal of a square =√2*side of square
=> side =Diagonal/(√2)
Area of square =s*s
 =(diagonal^2)/2

Difference of both tv's =(34^2-27^2)/2
 =427

BrentGMATPrepNow · Answer

If we take a  square  with side length x and draw a diagonal, we get two isosceles right triangles. 
If we focus on one such right triangle, we see that the legs have length x.

square 34-inch flat-screen television  
The diagonal (hypotenuse) = 34
So, we can apply the Pythagorean Theorem to get x² + x² = 34²
Simplify: 2x² = 34²
Divide both sides by 2 to get: x² = 34²/2
Since the area of the square = x², we can see that the area of this square is  34²/2

square 27-inch flat-screen television  
The diagonal (hypotenuse) = 27
So, we can apply the Pythagorean Theorem to get x² + x² = 27²
Simplify: 2x² = 27²
Divide both sides by 2 to get: x² = 27²/2
Since the area of the square = x², we can see that the area of this square is  27²/2

DIFFERENCE IN AREAS =  34²/2  -  27²/2

IMPORTANT : Before we perform any calculations, SCAN the answer choices. 
Now notice that  34²/2  =  (some EVEN integer)/2  =  SOME INTEGER 
Also, notice that  27²/2  =  (some ODD integer)/2  =  SOMETHING.5

So,  34²/2  -  27²/2  =  SOME INTEGER  -  SOMETHING.5 
= something.5
Perfect - only answer choice works!!

Answer:  B

RELATED VIDEO: 
 https://www.youtube.com/watch?v=iUUP2sp4ogg

paidlukkha · Answer

Missed to divide 
427/2 =213.5

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paidlukkha · Answer

213.5 is giving only the half difference on the side of 2 squares

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DAllison2016 · Answer

d_1 = 34\
d_2 = 27

From Pythagoras:  \sqrt{a^2 + b^2} = d .
For Pythagoras on a square,  a=b \implies \sqrt{2a^2} = d 
Area of a square:  a^2 , in this case:  a^2 = \frac{d^2}{2} 
Subtract the two areas to obtain the formula:  \frac{d_1^{\,2}}{2} - \frac{d_2^{\,2}}{2} 
 = \frac{1}{2}(d_1^{\,2}-d_2^{\,2}) 
 = \frac{1}{2}(1156 - 729) = \frac{427}{2} = 213.5

D

Divyadisha · Answer

Area of square= diagonal^2/2

How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television?
34^2/2- 27^2/2

units digit of 34^2= 6
Units digit of 27^2= 9

6-9 will generate 7 as the units digit and 7/2 will generate .5 at the end. Only option B has this form.

B is the answer

LogicGuru1 · Answer

Diagonal is x√2

For bigger 34 inch TV
Diagonal x√2=34 
Side x=34/√2
Area x^2= 34^2 /2

For Smaller 27 inch TV
Diagonal x√2=27 
Side x=27/√2
Area x^2= 27^2 /2

Difference = (1156-729)/2 = 427/2 = 213.1

Answer is B

bumpbot · Answer

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