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If the length of two sides of a triangle are 6 and 8 units, which of t
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18 Nov 2021, 04:09
18 Nov 2021, 04:09
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If the length of two sides of a triangle are 6 and 8 units, which of the following cannot be the area of the triangle in square units ?
A. 0.01
B. 5
C. 10
D. 20
E. 25
GRE Tips and Tricks - UPDATED 11/15/2021
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
A. 0.01
B. 5
C. 10
D. 20
E. 25
GRE Tips and Tricks - UPDATED 11/15/2021
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
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Joined: 09 Nov 2021
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Re: If the length of two sides of a triangle are 6 and 8 units, which of t
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18 Nov 2021, 05:11
18 Nov 2021, 05:11
1
Think about it like this: the area depends on the base and the height. The maximized base and height would be when the base and height are perpendicular to one another. Note that any configuration other than this will decrease the height while retaining the base (or vice-versa).
Depending on how small the angle is between the side of 6 and the side of 8, we can get what is essentially an infinitely small area.
That means you'd have a 6:8:10 right triangle.
This gives a maximized area of (1/2)bh = (1/2)(6*8) = (1/2)*48 = 24.
If the maximized area is 24, then we cannot have 25 as a possibility. The answer is E.
Depending on how small the angle is between the side of 6 and the side of 8, we can get what is essentially an infinitely small area.
That means you'd have a 6:8:10 right triangle.
This gives a maximized area of (1/2)bh = (1/2)(6*8) = (1/2)*48 = 24.
If the maximized area is 24, then we cannot have 25 as a possibility. The answer is E.
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Re: If the length of two sides of a triangle are 6 and 8 units, which of t
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18 Nov 2021, 06:17
18 Nov 2021, 06:17
1
Carcass wrote:
If the length of two sides of a triangle are 6 and 8 units, which of the following cannot be the area of the triangle in square units ?
A. 0.01
B. 5
C. 10
D. 20
E. 25
A. 0.01
B. 5
C. 10
D. 20
E. 25
We can actually solve this question without using any triangle properties.
First recognize that we can take the two given sides (with lengths 6 and 8) and make them super close together so that the resulting triangle is very very narrow.
In other words, we can take the two given sides and make the area of the triangle approach zero.
So, there's no minimum value for the area of the triangle.
There is, however, a maximum value for the area of the triangle, which means the correct answer must be E (since it's the biggest option)
