Data Sufficiency

B

The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM.

1) x is 4 times y.
2) x is 4 times greater than y.

How are two different? Please clarify.

Thanks.

Someone please respond to the following query:

The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM.

1) x is 4 times y.
2) x is 4 times greater than y.

How are two different? Please clarify.

Thanks
Mankey

Statement 1:

THis in addition with the problem statement makes the Triangles similar this is sufficient to answer the question

Statement 2: Gives only the area of ABC=96=1/2x*y which can have several combinations. SO insufficient

The formula for the Area of a triangle is 1/2 BASE X ALTITUDE.

Stmt 1 : If the angles ABC and KLM are equal, the triangles are similar triangles.

1/2 BC * AC = 4 * 1/2* LM * KM
BC * AC = 4 LM * KM
= 2 LM * 2 KM

Observe that the length of sides double when the Area increases (SIMILAR TRIANGLES)
Hence the Hypotenuse will be 2* 10 inches = 20 inches.

Stmt 2 : LM = 6 inches. Not sufficient because the length does one ensure they are similar triangles.

Hence Ans A.

Answer is A.
Both triangle are similar. So ratio of lengths of sides of triangles should be same.

s1 says that the trianagles are similar and hence can find the sides of each of the triangle using trigonometric equations
s2 only tells us about triangle KLM, nothing is known about triangle ABC

Hence (A) is ans

So what is the OA?

Im On C


the case may be that 8b*1/2h..Then the Option A would be wrong.

S1 is sufficient as by two angles are same means the triangles are similar and then by using trigonometric relations, one can find the hypotenuse of the other triangle

(A) is the answer

Sorry, to chime in on this, as it almost seems irrelevant to the conversation, Statement (1) indicates that ABC and KLM both = 55 degrees. Does it matter where the sides are positioned or where the vertex is that measures the 55 degrees. I may be thinking into it too much, but just want to understand the only items I need to determine if it can be answered. Thanks!

mankey wrote:The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM.

1) x is 4 times y.
2) x is 4 times greater than y.

How are two different? Please clarify.

Thanks.

1 => x=4y
2 => means x-y=4y => x=5y

So we should have memorized the common right triangle sides... 3:4:5-->6:8:10. From the prompt, we know that right triangle KLM has sides 6:8:10. This isn't necessary information, it's just good to realize it.

The rule that is important to know is:
With similar triangles, the ratio of area= s^2:s^2

We DON'T know is whether these are similar triangles. If they are (all their angles are the same), then we can figure this problem out.
1) Since we already know they're both right traingles, it means that one of their angles is 90 degrees. If they both also have a 66 degree angle, it means that their last angle is 35. Then YES, these two triangles ARE SIMILAR. SUFFICIENT.

2) We already know this from the prompt. Nothing new here.. INSUFFICIENT.

A is correct.

Properties of Similar Triangles:

"¢ Corresponding angles are the same.
"¢ Corresponding sides are all in the same proportion.
"¢ It is only necessary to determine that two sets of angles are identical in order to conclude that two triangles are similar; the third set will be identical because all of the angles of a triangle always sum to 180º.
"¢ If two similar triangles have sides in the ratio x/y, then their areas are in the ratio x^2/y^2.

Statement 2
Angles ABC and KLM are each equal to 55 degrees --> ABC and KLM are similar triangles --> area(ABC)/area(KLM) = 1/4, so the sides are in ratio 2/1 --> hypotenuse KL=10 --> hypotenuse AB=2*10=20.
Sufficient

Statement 1
LM is 6 inches --> KM=8 --> area(KLM) = 24 --> area(ABC) = 96. But just knowing the area of ABC is not enough to determine hypotenuse AB. For instance: legs of ABC can be 96 and 2 OR 48 and 4 and you'll get different values for hypotenuse.
Not sufficient

A

A in answer.

(AB)^2/(10)^2=4+1

(AB)^2=500

AB=(500)^(1/2)