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To find: the perimeter of ∆ABC?

Solution:
First Rule: Never Imagine Answer Yourself.
We often forget this, and end up selecting wrong option.

1) AB = 3 and BC = 5
Though this looks like perfect 3,4,5 triplet of right angle triangle. How can you say its a right angle triangle.
Neither 3rd side is mentioned nor any angle among triangle.
We can't speculate its a right angle triangle with third side as 4 and perimeter as 12. (Insufficient)

2) Area of ∆ABC = 6
Area = 1/2*base*height....
6 = 1/2*base*height
12 = base*height
The order pair of base and height (B,H) = (12*1),(6*2),(4*3),(3*4),(2*6),(1*12)
Definitely not sufficient.
(Insufficient)

Statement 1&2: even though the imaginary part already took 3,4,5 as the triangle side. But we don't have the third side.
Only side 3 is common not other two.
=> 3,4 triangle can have 6 as side 3rd.
=> 3,5 triangle can have 7 as side 3rd.
We can't predict it's 3,4,5 triplet by this.

Hence only E option can be the answer.

Posted from my mobile device
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(I was WRONG).
IMO Answer is C, and the only possible answer is that AC=4.

h*ab/2=6
Hence h=4
By definition h creates a 90 degree angle with the base (AB). So we know h=4, AB=3, AND that there is a 90° angle between them. This is enough to calculate AC.

If you calculate BC*h/2=6 you will get a messy h=2.4 and you will need to calculate first where h splits the base (BC). This is a little bit more complicated but you will get to the same answer at the end.

Posted from my mobile device
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GMATinsight
Find the perimeter of ∆ABC?

1) AB = 3 and BC = 5
2) Area of ∆ABC = 6

OFFICIAL EXPLANATION

Answer: Option E

Check the step-by-step video explanation


Attachments

Screenshot 2020-07-03 at 12.04.12 PM.png
Screenshot 2020-07-03 at 12.04.12 PM.png [ 804.73 KiB | Viewed 3771 times ]

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Gabzev25
WRONG.
IMO Answer is C, and the only possible answer is that AC=4.

h*ab/2=6
Hence h=4
By definition h creates a 90 degree angle with the base (AB). So we know h=4, AB=3, AND that there is a 90° angle between them. This is enough to calculate AC.

If you calculate BC*h/2=6 you will get a messy h=2.4 and you will need to calculate first where h splits the base (BC). This is a little bit more complicated but you will get to the same answer at the end.

Posted from my mobile device

HI Gabzev25

I have posted the explanation for clarity. The correct answer is Option E

Several suggestions on your post

1) Base is not any particular side but it's upto us which side we consider the Base. Height is always
2) Refer to the attached image in my previous post to understand second triangle with two sides 3 and 5 and area=6
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Babineaux
From statement 1:

AB = 3 and BC = 5

From here we can't clearly say whether this is right, acute or obtuse angled.

Thus, insufficient.

From statement 2:

For the area given is 6, we can't say anything.

Combining,

If we consider a height of h,

Thus by taking the smallest side say 3 here and h and given area 6;

We can determine h = 4

And now taking other side 5, we can clearly say that h is nothing but the third side, forming a right angled triangle of 3, 4, and 5 unit length.

From here we can determine the perimeter of the triangle.

IMO ans is C.

Posted from my mobile device
the question doesnt say that the side has to be an integer, there could be various root values, and it shows inconsistency. therefore E
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you can also use hero's formula to find the area of triangle (s(s-a)(s-b)(s-c))^0.5 and s =(a+b+c)/3... so with the help of statement A, we can use value of 2 variables and find the third on by using this formula...so i think "C" would be the best option[/i]
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