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30 Oct 2025, 11:08
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
66% (01:45) correct
33% (01:17) wrong based on 3 sessions
History
Date
Time
Result
Not Attempted Yet
Quantity A
The greatest possible area of a triangle with side lengths 4, 5, and x
Quantity B
11
The greatest possible area of a triangle with side lengths 4, 5, and x
Quantity B
11
02 Nov 2025, 11:27
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Official Explanation
If the two known sides of length 4 and 5 are placed perpendicular to each other, they can be used as the base and height to compute the triangle’s area as,
by the formula area =
Now imagine using the side of length 5 as the base and swiveling the side of length 4, about a hinge at the vertex of the triangle where these sides intersect. The resulting height, h, in the figures above, is less than 4, whether the triangle is acute or obtuse. (It should be obvious that h < 4 in the two diagrams at right, above, but if you are not sure why, observe that h is the leg of a smaller right triangle, which has hypotenuse = 4.) Then the area of the right triangle, 10, is the maximum possible, and (B), 11 is greater.
Answer: B
GMAT-Club-Forum-qs3uy15f.png [ 26.94 KiB | Viewed 211 times ]
GMAT-Club-Forum-ge2r5ik1.png [ 15.43 KiB | Viewed 210 times ]
If the two known sides of length 4 and 5 are placed perpendicular to each other, they can be used as the base and height to compute the triangle’s area as,
by the formula area =
Now imagine using the side of length 5 as the base and swiveling the side of length 4, about a hinge at the vertex of the triangle where these sides intersect. The resulting height, h, in the figures above, is less than 4, whether the triangle is acute or obtuse. (It should be obvious that h < 4 in the two diagrams at right, above, but if you are not sure why, observe that h is the leg of a smaller right triangle, which has hypotenuse = 4.) Then the area of the right triangle, 10, is the maximum possible, and (B), 11 is greater.
Answer: B
Attachment:
GMAT-Club-Forum-qs3uy15f.png [ 26.94 KiB | Viewed 211 times ]
Attachment:
GMAT-Club-Forum-ge2r5ik1.png [ 15.43 KiB | Viewed 210 times ]
