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gmatbusters

What is the area of the triangle above?
(1) \(a^2\)+ 9 = 25
(2) x = 90 deg



Attachment:
DS1.jpg


Question stem: Ares of the above triangle?

From statement 1:

\(a^2 = 16\)
a = +4 or -4.
Since the side of a triangle can NEVER be negative. a = 4.
Now, by looking at the triangle, we can see that it's a right angled triangle. Hence area can be found using the formula 1/2*b*h = 1/2*4*3 = 6.
Sufficient.

From statement 2:

Angle x = 90.
Then the triangle becomes a right-angled triangle.
By Pythagorean theorem, we get a as 4. and area = 1/2*b*h = 1/2*4*3 = 6.
Sufficient.

D is the answer.
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gmatbusters

What is the area of the triangle above?
(1) \(a^2\)+ 9 = 25
(2) x = 90 deg



Attachment:
DS1.jpg


This question is all about Pythagorean triplets . Mark the length of the legs of this triangle. 3 - 4 -5 . use this triplets to find out the area.

Statement 1: \(a^2 = 5^2 - 3^2\). a = 4. Sufficient .

Statement : x =90 degree. Match the angle with 3 -4 -5. it's a right triangle. Sufficient.

The best answer is D.
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GMATBusters

What is the area of the triangle above?
(1) \(a^2\)+ 9 = 25
(2) x = 90 deg



Attachment:
DS1.jpg

(1) \(a^2 = 16\) or \(a = 4\). Now we know that \(3-4-5\) is a right angle triangle. Therefore, \( x = 90°\) and \(area = 1/2*3*4 = 6\) Sufficient

(2) \(x = 90°\) means we can apply pythagoras theorem. \(3^2+a^2=5^2\) therefore \(a = 4\), therefore \(area = 1/2*3*4 = 6\) Sufficient

Hence, option D.
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