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The greatest possible area of a triangle with side lengths 4, 5, and x

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The greatest possible area of a triangle with side lengths 4, 5, and x [#permalink] New post   13 Oct 2021, 07:25
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Quantity A
Quantity B
The greatest possible area of a triangle with side lengths 4, 5, and x
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A) Quantity A is greater.
B) Quantity 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] New post   13 Oct 2021, 11:59
with given setting we can form right angle triangle 3-4-5 , as we know area of triangle is 1/2 * height*base = 0.5*4*3=6.
i am not sure about explanation but looking forward for expert explanation. Actually on first attempt i got incorrect. So, my explanation might be have loose ends.
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The greatest possible area of a triangle with side lengths 4, 5, and x [#permalink] New post   13 Oct 2021, 19:49
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The area of a triangle is the greatest when it is the right-angled triangle.

Let's consider 4 & 5 as the perpendicular sides of a right-angled triangle.

Maximum Area \(= \frac{1}{2} * 4 * 5 = 10\)

Qt B \(>\) Qt A

Answer B
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Re: The greatest possible area of a triangle with side lengths 4, 5, and x [#permalink] New post   22 Nov 2022, 08:24
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rx10 wrote:
The area of a triangle is the greatest when it is the right-angled triangle.

Let's consider 4 & 5 as the perpendicular sides of a right-angled triangle.

Maximum Area \(= \frac{1}{2} * 4 * 5 = 10\)

Qt B \(>\) Qt A

Answer B


Helo,
there is a small doubt i'm having in this explanation, how can the area of a triangle is the greatest when it is the right-angled triangle.
can someone give me diagramatic explanation.
and why we need to consider 4 and 5 as the perpendicular sides why not hypothenuse.
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Re: The greatest possible area of a triangle with side lengths 4, 5, and x [#permalink] New post   24 Nov 2022, 09:31
what is the proper algorithm here? Both the provided solutions are quite intuitive
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Re: The greatest possible area of a triangle with side lengths 4, 5, and x [#permalink] New post   25 Nov 2022, 06:53
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In Qt A, we are asked to find the greatest possible area.

Now consider a case where 5 is the hypotenuse. So the sides will be 3 & 4. Even if you consider that case, the area of the triangle will be 6.

As we are told to go for the maximum area, we should look out for all the reasons to get Qt A either equal to or greater than Qt B so that we can arrive at the answer.

So in this case, how much more we try, we will end up getting 10 as the highest area. You can consider any other triangle. But area of the right-angled one is always the greatest. Hope this helps!


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Re: The greatest possible area of a triangle with side lengths 4, 5, and x [#permalink] New post   13 Apr 2024, 07:26
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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