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The greatest possible area of a triangle with side lengths 4, 5, and x
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02 Jul 2021, 05:37
02 Jul 2021, 05:37
Expert Reply
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Question Stats:
57% (01:19) correct
42% (01:28) wrong based on 59 sessions
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Quantity A |
Quantity B |
The greatest possible area of a triangle with side lengths 4, 5, and x |
11 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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Re: The greatest possible area of a triangle with side lengths 4, 5, and x
[#permalink]
02 Jul 2021, 07:29
02 Jul 2021, 07:29
1
Triangle has greatest area when it is right triangle triangle, considering this, maximum area would be :
>> 1/2 *b*h
>>1/2 *4*5
>>10
Hence, quantity B is greater.
>> 1/2 *b*h
>>1/2 *4*5
>>10
Hence, quantity B is greater.
Re: The greatest possible area of a triangle with side lengths 4, 5, and x
[#permalink]
05 Jul 2021, 19:52
05 Jul 2021, 19:52
The area of a triangle is maximum when one of the three angles is 90° because then the height is maximum, otherwise it is maximum when all the three sides are equal or the triangle is equilateral triangle.
So the maximum possible height for this can be 5 and then the base have to be 4 so that the hypotenuse be greater than that.
So the maximum possible area of this triangle is (5*4)/2=10
So B is greater.
So the maximum possible height for this can be 5 and then the base have to be 4 so that the hypotenuse be greater than that.
So the maximum possible area of this triangle is (5*4)/2=10
So B is greater.
