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
OA is E.
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Difference of areas of 2 TVs
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pareekbharat86
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Size = Diagnol = side * sqrt(2)
Area of 21 inch - Area of 19 Inch
(21/sqrt(2))^2 - (19/sqrt(2))^2
1/2 (21+19)(21-19) = 1/2 * 40 * 2 = 40
Answer [spoiler]{E}[/spoiler]
Area of 21 inch - Area of 19 Inch
(21/sqrt(2))^2 - (19/sqrt(2))^2
1/2 (21+19)(21-19) = 1/2 * 40 * 2 = 40
Answer [spoiler]{E}[/spoiler]
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ganeshrkamath
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The diagonal of a square with sides of length a = a sqrt(2)pareekbharat86 wrote: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
OA is E.
Area of the square = a^2 = (diagonal^2)/2
Area of 21-inch screen = 1/2 * 21^2
Area of 19-inch screen = 1/2 * 19^2
Difference = 1/2 * (21^2 - 19^2)
= 1/2 * (21 + 19) * (21 - 19)
= 1/2 * (40) * (2)
= 40 sq. inches
Choose E
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Hi pareekbharat86,
Rahul has properly explained the math behind this question. Here's the pattern that you need to know:
GMAT geometry questions emphasize certain formulas and relationships. Here, it's worth noting that EVERY square can be broken down into 2 45/45/90 triangles.
45/45/90 triangles have a relationship among their sides: X/X/X(root2)
Be on the lookout for this rule, as it's likely to be something that you're tested on during your Official GMAT.
GMAT assassins aren't born, they're made,
Rich
Rahul has properly explained the math behind this question. Here's the pattern that you need to know:
GMAT geometry questions emphasize certain formulas and relationships. Here, it's worth noting that EVERY square can be broken down into 2 45/45/90 triangles.
45/45/90 triangles have a relationship among their sides: X/X/X(root2)
Be on the lookout for this rule, as it's likely to be something that you're tested on during your Official GMAT.
GMAT assassins aren't born, they're made,
Rich
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GMATGuruNY
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We can save a little time if we know the following:pareekbharat86 wrote: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
The area of a rhombus with diagonals d� and d₂ = (d�d₂)/2.
A square is a rhombus with 4 equal angles.
In a square, the two diagonals are equal.
Thus, the area of a square with diagonal d = d²/2.
a² - b² = (a+b)(a-b).
Thus:
Big TV - Little TV = 21²/2 - 19²/2 = (1/2)(21² - 19²) = (1/2)(21+19)(21-19) = 40.
The correct answer is E.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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pareekbharat86
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Thanks all of you.
My brain's got so fried with so much practicing that I kept getting 20 as the answer. I was using 1/2*base*height formula for a square!!! My bad.
My brain's got so fried with so much practicing that I kept getting 20 as the answer. I was using 1/2*base*height formula for a square!!! My bad.
Thanks,
Bharat.
Bharat.
in above solutions it is clear the the difference between both areas can be calculated as:
Difference = 1/2 * (21^2 - 19^2) ..... (A)
here i wana advise a general way to calculate the difference between to squares.
i.e
(n+1)^2 - n^2 = 2n+1
(n+2)^2 - n^2 = 2(2n+2)
(n+3)^2 - n^2 = 3(2n+3)
.....
so here we may consider 19 as "n" so "n+2" is 21.
and difference in area is
Difference = 1/2 * (21^2 - 19^2):
Difference = 1/2 * (19+2)^2 - 19^2 = 1/2 * 2(2*19+2)= 40
this is more efficient way to find difference between big squares.
hope you like.
Difference = 1/2 * (21^2 - 19^2) ..... (A)
here i wana advise a general way to calculate the difference between to squares.
i.e
(n+1)^2 - n^2 = 2n+1
(n+2)^2 - n^2 = 2(2n+2)
(n+3)^2 - n^2 = 3(2n+3)
.....
so here we may consider 19 as "n" so "n+2" is 21.
and difference in area is
Difference = 1/2 * (21^2 - 19^2):
Difference = 1/2 * (19+2)^2 - 19^2 = 1/2 * 2(2*19+2)= 40
this is more efficient way to find difference between big squares.
hope you like.
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vipulgoyal
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