ABC is a right angle triangle, which is 90 degree at A.

Question

ABC is a right angle triangle, which is 90 degree at A. What is the Area of the triangle ABC?

1) AB + AC = 8.
2) The largest side is 5 \sqrt{2} .

Kurtosis · Answer

Triangle is right angled at A. So BC is the hypotenuse.
Area = 1/2*(AB)*(AC)

St1: AB + AC = 8 --> Not sufficient as we get multiple possibilities for AB and AC

St2: BC = 5*sqrt(2) --> Not sufficient to determine the area

Combining St1 and St2,
AB^2 + AC^2 = BC^2......(1)
AB + AC = 8 and BC = 5*sqrt(2)
Only AB = 7, AC = 1 or AC = 7, AB = 1 satisfies (1). Thus AB*AC = 7. Area can be found out
St1 and St2 together is sufficient

Answer: C

Lorenzo3688 · Answer

ABC is a right angle triangle, which is 90 degree at A. What is the Area of the triangle ABC?
1) AB + AC = 8.
2) The largest side is 52√.

AB^2 + AC^2 = BC^2......(1)
AB + AC = 8 and BC = 5*sqrt(2)
Only AB = 7, AC = 1 or AC = 7, AB = 1 satisfies (1). Thus AB*AC = 7. Area can be found out
St1 and St2 together is sufficient

Answer: C

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

ABC is a right angle triangle, which is 90 degree at A. What is the Area of the triangle ABC?
 
1) AB + AC = 8.
2) The largest side is 5 √ 2

When you modify the original condition and the question, for the right angle triangle, there are 2 variables(the base line and height), which should match with the number of equations. So you need 2 equations. For 1) 1equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), they become AB^2+AC^2=(5√2)^2=50, (AB+AC)^2=8^2=64, AB^2+AC^2+2AB*AC=64 → 50+2AB*AC=64, AB*AC/2=7/2, which is unique and sufficient. 
Therefore, the answer is C.

--> For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

Lorenzo3688 · Answer

ABC is a right angle triangle, which is 90 degree at A. What is the Area of the triangle ABC?
1) AB + AC = 8.
2) The largest side is 52√.

AB^2 + AC^2 = BC^2......(1)
AB + AC = 8 and BC = 5*sqrt(2)
Only AB = 7, AC = 1 or AC = 7, AB = 1 satisfies (1). Thus AB*AC = 7. Area can be found out
St1 and St2 together is sufficient

Answer: C

ArunpriyanJ · Answer

Understood...But when similar question with different Question is given....I have to try with the different no's and if i get two pairs solving the equation, then i should choose 'E'.

Pls correct if my understanding is wrong.

Thanks,
A

ENGRTOMBA2018 · Answer

If there is another question that asks you the area of triangle ABC without telling you which one is the right angle, then yes, there is a high probability that E will be the answer. You have to take it on a case by case basis.

Hope this helps.

meganbailey · Answer

Why isn't the answer B? If the longest side (hypotenuse) is 5sq.rt.2, then wouldn't that make the other 2 sides 5 and 5?

chetan2u · Answer

hi

there will be numerous ways /triangles where hypotenuse is  5\sqrt{2} ..
 a^2+b^2=(5\sqrt{2})^2......a^2+b^2=50 
say a is 7, b will be 1
a is 6, b will be  \sqrt{50-36}=\sqrt{24}=2\sqrt{6}

hope it helps

bumpbot · Answer

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ABC is a right angle triangle, which is 90 degree at A.

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ABC is a right angle triangle, which is 90 degree at A.

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