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What is the area of the triangle above?

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What is the area of the triangle above? [#permalink] New post   08 Nov 2018, 09:45
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What is the area of the triangle above?

(1) \(a^2\)+ 9 = 25
(2) x = 90 degrees

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What is the area of the triangle above? [#permalink] New post   08 Nov 2018, 10:09
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gmatbusters wrote:

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



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DS1.jpg



(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.
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Re: What is the area of the triangle above? [#permalink] New post   08 Nov 2018, 10:37
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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What is the area of the triangle above? [#permalink] New post   08 Nov 2018, 11:12
gmatbusters wrote:

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


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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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What is the area of the triangle above? [#permalink] New post   08 Nov 2018, 13:03
gmatbusters wrote:

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


Show Spoiler
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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What is the area of the triangle above? [#permalink] New post   16 Feb 2022, 06:47
GMATBusters wrote:

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


Show Spoiler
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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What is the area of the triangle above? [#permalink]
16 Feb 2022, 06:47
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