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11 Jun 2022, 09:45
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
42% (02:51) correct
58%
(02:53)
wrong
based on 19
sessions
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Date
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Not Attempted Yet
Rectangle ABCD has AB =8 and BC = 6. Point M is the midpoint of diagonal AC, and E is on AB with ME perpendicular to AC. What is the area of triangle AME?
(A) 65/8
(B) 25/3
(C) 9
(D) 75/8
(E) 85/8
Are You Up For the Challenge: 700 Level Questions
(A) 65/8
(B) 25/3
(C) 9
(D) 75/8
(E) 85/8
Are You Up For the Challenge: 700 Level Questions
PyjamaScientist
Admitted - Which School Forum Moderator
Joined: 25 Oct 2020
Last visit: 04 Apr 2026
Posts: 1,125
Own Kudos:
Given Kudos: 633
Schools: Ross '25 (M$)
GMAT 1: 740 Q49 V42 (Online)
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12 Jun 2022, 03:47
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MissBong
Joined: 02 Apr 2021
Last visit: 15 Jan 2025
Posts: 55
Given Kudos: 167
Location: India
Schools: Tepper '25 (A$) Ross '25 (M)
GMAT 1: 720 Q49 V38 (Online)
12 Jun 2022, 11:39
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\(AC^2\) =\(AB^2\) +\( BC^2\)
AC= 10
If we consider \(\angle\) BAC = \(\alpha \),
then tan \(\alpha\) = \(\frac{6}{8}\)
We can also write tan \(\alpha\) = \(\frac{ME}{5}\) [ 5, because M is mid point of AC]
Therefore,\(\frac{ME}{5}\)=\(\frac{6}{8}\)
ME= \(\frac{30}{8}\)
Area=\( \frac{1}{2}\)* Base * Height =\(\frac{1}{2}\)* AM* ME = \(\frac{1}{2}\)*5*\(\frac{30}{8}\)
Area =\(\frac{75}{8} \) (D)
AC= 10
If we consider \(\angle\) BAC = \(\alpha \),
then tan \(\alpha\) = \(\frac{6}{8}\)
We can also write tan \(\alpha\) = \(\frac{ME}{5}\) [ 5, because M is mid point of AC]
Therefore,\(\frac{ME}{5}\)=\(\frac{6}{8}\)
ME= \(\frac{30}{8}\)
Area=\( \frac{1}{2}\)* Base * Height =\(\frac{1}{2}\)* AM* ME = \(\frac{1}{2}\)*5*\(\frac{30}{8}\)
Area =\(\frac{75}{8} \) (D)
