What is the area of right triangle ABC ?

Question

(1) The hypotenuse of △ABC is 13. 
(2) The perimeter of △ABC is 30.

Are You Up For the Challenge: 700 Level Questions

Project DS Butler Data Sufficiency (DS3) 
 For DS butler Questions  Click Here

yashikaaggarwal · Answer

(1) The hypotenuse of △ABC is 13.
H^2 = S1^2 + S2^2
13^2 = S1^2 + S2^2

Case 1: sides are equal.
13^2 = S1^2 + S1^2
13^2 = 2S1^2
13^2/2 = S1^2
13/√2 = S (area will be 169/4 = 42.25)

Case 2: 5,12,13 (right angle triangle triplet)
area will be 
1/2*12*5 = 30 
(Insufficient)

(2) The perimeter of △ABC is 30.
There can be many integral or non integral right angle triangle triplet from perimeter 30.
(Insufficient)

Combining both: hypotenuse = 13
So the length of other two sides = 17

Case 1: sides are equal.
13^2 = S1^2 + S1^2
13^2 = 2S1^2
13^2/2 = S1^2
13/√2 = S
13/√2+13/√2 ≠ 17 (Incorrect)

Case 2: 5,12,13 (right angle triangle triplet)
12+5 = 17 (Correct)
Then area will be 
1/2*12*5 = 30 
(Sufficient)

IMO C

Posted from my mobile device

v12345 · Answer

Statement 1: Insufficient
We don't get value of any other side.
Statement 2: Insufficient
Sides can have different measures.

Combining, Sufficient
Hypotenuse = 13
Other sides = 12 and 5
Area of ABC = 30

Hence, OA is (C).

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • ABC is a right triangle.
• Let us assume that in triangle ABC :
 o Base = a
o Height = b
o And, hypotenuse = c
    a^2 + b^2 = c^2…..Eq.(i)   
• We need to find the area of ABC 
 o i.e. we need to find the value of   \frac{1}{2}*a*b

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  The hypotenuse of △ABC is 13.
 • According to this statement: c = 13
• However, we cannot find a and b from here, and hence cannot find the area. 
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2:  The perimeter of △ABC is 30.
 •  a + b + c = 30 ……Eq.(ii) 
• We have 3 unknowns and only two equations (i.e. Eq.(i) and Eq.(ii)), so we cannot find the value of a and b. 
Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.

Step 3: Analyse Statements by combining. 
 • From statement 1: c = 13
• From statement 2: a + b + c = 30
• On combining both statements , we get,
 o  a + b = 17  
o  ⟹ (a+b)^2 = 17^2 
o   ⟹ a^2 + b^2 +2a*b = 17^2 
o   ⟹ c^2 + 2*a*b = 17^2   
o   ⟹ 2*a*b = 17^2 – 13^2  
o   ⟹ \frac{1}{2}*a*b = \frac{17^2 – 13^2}{4}   
Thus, the correct answer is  Option C.

sood1596 · Answer

Question: 1/2 * x*y =?
Value of x and y or x*y

Statement 1 - X^2 + y^2 = 13^2
Do not know value of x and y
Insufficient

Statement 2 - x + y + z = 30
No values given
Insufficient

1 & 2

X^2 + y^2 = 13^2 (...1)
z = 13

x + y = 30-13 = 17
sq both sides
X^2 + y^2 + 2xy = 17^2 (..2)
Substitute 1 in 2
2xy = 17^2 - 13^2

Since we can find value of xy

Sufficient

Answer - C

KaramveerBakshi · Answer

Area = 1/2*l*b

Statements:

(1) The hypotenuse of △ABC is 13.
We know nothing about the other two sides.

Insufficient

(2) The perimeter of △ABC is 30.
a+b+c = 30.
Can have varied sides.

Insufficient

Combining, we get:

a+b+c= 30 ---- (A)
c = 13 ----- (B)
Also, we know a^2+b^2 = c^2 ---- (C)

(A), (B), and (C) gives us

a^2 + (17-a)^2 = 13^2

We can get a (+ve) and so the area.

Sufficient

Hence, the answer is Option (C).

sambitspm · Answer

Kindly see the attachment.
  The question is easy but the most common error is when you try to formalize equation in Part B. Also, the roots need to be calculated correctly, otherwise, you might spend some extra time on this question.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

What is the area of right triangle ABC ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

What is the area of right triangle ABC ?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards