enigma123 wrote:
The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM. If the hypotenuse KL is 10 inches, what is the length of the hypotenuse AB?
(1) Angles ABC and KLM are each equal to 55 degrees.
(2) LM is 6 inches.
Below are the properties of similar triangles you might find useful for the GMAT and the solution which calculates the actual value of AB.
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
\frac{x}{y}, then their areas are in the ratio
\frac{x^2}{y^2}.
OR in another way: in two similar triangles, the ratio of their areas is the square of the ratio of their sides:
\frac{AREA}{area}=\frac{SIDE^2}{side^2}.
Back to original question:
Attachment:
KLM Triangle.GIF [ 2.03 KiB | Viewed 983 times ]
The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM. If the hypotenuse KL is 10 inches, what is the length of the hypotenuse AB? (1) Angles ABC and KLM are each equal to 55 degrees --> ABC and KLM are similar triangles -->
\frac{AREA_{ABC}}{area_{KLM}}=\frac{4}{1}, so the sides are in ratio 2/1 --> hypotenuse KL=10 --> hypotenuse AB=2*10=20. Sufficient.
(2) LM is 6 inches --> KM=8 -->
area_{KLM}=24 -->
AREA_{ABC}=96. But just knowing the are 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.
Answer: A.
Hope it helps.
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