What is the third side of the ∆ABC with sides 3-5-x? 1) ∆ABC encloses

Question

What is the third side of the ∆ABC with sides 3-5-x? 1) ∆ABC encloses maximum area with its sides of length 3, 5 and x units 2) ∆ABC is a right triangle source : www.GMATinsight.com

aviddd · Answer

1) ∆ABC encloses maximum area with its sides of length 3, 5 and x units
Area of a triangle is maximum when two sides are perpendicular, so this is a right angle triangle.

5 can be the hypotenuse, which makes x = 4. But if x is hypotenuse, then x is sqrt (9 + 25).

Insufficient.

2) ∆ABC is a right triangle

This gives us the same information which 1 gave. Nothing new.

Insufficient.

Combining both together, still insufficient. Answer: E

erv20 · Answer

aviddd  since we know that this is a right triangle, then don't we know from Pythagoras that x=4? why do we need to test if x is the hypotenuse?

aviddd · Answer

Looks like the OA is A, so I might be wrong.

It is a right angled triangle, but we don't know which side is hypotenuse. It cannot be 3 since it is less than 5. So hypotenuse can be 5 or x, depending on value of x.

aviddd · Answer

Why is the answer A?

AJ0784 · Answer

statment 1: For maximum area the third side must be 7 which also satisfies the sides condition of a triangle. SUFFICIENT

Statement 2 : Can not be confirmed out of 5 or x which is the hypotenuse. NOT SUFFICIENT

Hence answer is A.

GMATStudyStudent · Answer

Statement 1:

For maximum area, the angle between the two given sides 3 and 5 should be 90. Therefore, length of 3rd side =  \sqrt{3^2 + 5^2}

SUFFICIENT

Statement 2:

The third side could be x=4 in 3-4-5 triangle or the x= \sqrt{3^2 + 5^2}

INSUFFICIENT.

IMO: A

rusanovmp · Answer

1) it says "1) ∆ABC encloses maximum area with its sides of length 3, 5 and x units" - it will happen with right triangle:

Let's consider 2 cases :
case 1 we have the area of the triangle where legs are 3 and 5 = 7.5 and x=5.83
case 2 we have the area of the triangle where legs are 3 and 4 = 6 and x=5 
It means that maximum area in the case 1, so x=5.83

so sufficient

2) Clearly insufficient

So the answer is A

bumpbot · Answer

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What is the third side of the ∆ABC with sides 3-5-x? 1) ∆ABC encloses

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What is the third side of the ∆ABC with sides 3-5-x? 1) ∆ABC encloses

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