What is the area of the triangle above?

Question

https://gmatclub.com/forum/download/file.php?id=44995 What is the area of the triangle above? (1) a^2 + 9 = 25 (2) x = 90 degrees DS1.jpg

u1983 · Answer

(1)  a^2 + 9 = 25 ==> a=4 ==> Now the three sides are 3,4,5 - a pythagorian triplet. Hence X=90 deg. Thus area =  \frac{1}{2} * 3 *4   - Sufficient 
(2) x = 90 deg ==> area =  \frac{1}{2} * 3 *a  ........and  a^2  = 5^2 -3^2 ==> a=4 ==>Hence, area = \frac{1}{2} * 3 *4   - Sufficient 
 Ans D .

dvishal387 · Answer

From statement 1 we can solve for a to get value as 4
As a^2=25-9=16
Area of triangle =0.5*b*h
=0.5*4*3=6
Sufficient
From statement 2 using pythagorean triplet we can get a=4 and get the area of triangle as in statement 1 above. sufficient
D should be the correct choice.

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Chethan92 · Answer

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.

KSBGC · Answer

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.

kungfury42 · Answer

(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.

What is the area of the triangle above?

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What is the area of the triangle above?

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