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Re: The greatest possible area of a triangle with side lengths 4, 5, and x [#permalink]
2
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]
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]
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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]
Hello from the GRE Prep Club BumpBot!

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