BTGmoderatorLU wrote:Source: Manhattan GMAT
In the figure, angle C and angle M are right angles, and KL = 10. If the area of triangle ABC is four times the area of triangle KLM, what is the length AB?
(1) Angles ABC and KLM have the same measure.
(2) LM is 6 inches.
Statement 1:
Since ∠C=∠M=90 and ∠ABC=∠KLM, the remaining two angles are also equal:
∠BAC=∠LKM.
Triangles with the same combination of angles are SIMILAR.
In similar triangles, corresponding sides in the SAME RATIO.
Here, AB and KL are corresponding sides, since each is a hypotenuse.
A rule for two similar triangles:
If each side in the larger triangle is x times the corresponding side in the smaller triangle, then the area of the larger triangle is x² the area of the smaller triangle.
In the case at hand:
Since the area of ∆ABC is 4 times the area of ∆KLM, each side in ∆ABC is 2 times the corresponding side in ∆KLM.
Since AB and KL are corresponding sides, we get:
AB = 2(KL) = 2*10 = 20.
SUFFICIENT.
Statement 2:
Thus, ∆KLM is a 6-8-10 triangle, implying that the area of ∆KLM = (1/2)(6)(8) = 24.
Since the area of ∆ABC is 4 times the area of ∆KLM, the area of ∆ABC = 4*24 = 96.
Implication:
(1/2)(AC)(BC) = 96
(AC)(BC) = 192.
It's possible that AC=1 and BC=192, in which case AB² = 1² + 192².
It's possible that AC=12 and BC=16, in which case AB² = 12² + 16².
Since AB can be different values, INSUFFICIENT.
The correct answer is
A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3