If a triangle has sides 8, 10, and z, which of the following cannot be the area of the triangle?
A) 3
B) 6
C) 12
D) 24
E) 46
OA: E
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Hi manik11,
When you have two sides of a triangle, the LARGEST possible area will occur when those two sides form the base and height of a right triangle. Any triangle OTHER than a right triangle that is formed with those 2 sides will have a SMALLER area.
Here, with an 8 and a 10, we COULD have an area of....
Area = (1/2)(8)(10) = 40
AND any area less than 40. So there's only one option here that CANNOT be the area of this triangle...
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
When you have two sides of a triangle, the LARGEST possible area will occur when those two sides form the base and height of a right triangle. Any triangle OTHER than a right triangle that is formed with those 2 sides will have a SMALLER area.
Here, with an 8 and a 10, we COULD have an area of....
Area = (1/2)(8)(10) = 40
AND any area less than 40. So there's only one option here that CANNOT be the area of this triangle...
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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OptimusPrep
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NOTE: For any two given sides, the largest area of the triangle will be when it is a right angled triangle with sides as base and heightmanik11 wrote:If a triangle has sides 8, 10, and z, which of the following cannot be the area of the triangle?
A) 3
B) 6
C) 12
D) 24
E) 46
OA: E
Maximum area = (1/2)*8*10 = 40
Of the given options, only option E is more than 40
Hence this cannot be the area of a triangle with sides 8, 10 and z
Correct Option: E
