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# Rectangle ABCD has AB =8 and BC = 6. Point M is the midpoint of diagon

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Math Expert
Joined: 02 Sep 2009
Posts: 58357
Rectangle ABCD has AB =8 and BC = 6. Point M is the midpoint of diagon  [#permalink]

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29 Mar 2019, 00:46
00:00

Difficulty:

75% (hard)

Question Stats:

47% (03:00) correct 53% (03:35) wrong based on 19 sessions

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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

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Re: Rectangle ABCD has AB =8 and BC = 6. Point M is the midpoint of diagon  [#permalink]

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29 Mar 2019, 03:51
2
By the Pythagorean theorem we have AC=10, hence AM=5.

The triangles AME and ABC have the same angle at A and a right angle, thus all their angles are equal,so two triangles are similar.

The ratio of their sides is AM/AB = 5/8, hence the ratio of their areas is (5/8)^2 = 25/64

And as the area of triangle ABC is (6*8)/2 = 24, the area of triangle AME is 24*(25/64) = 75/8

OA: (D)
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Joined: 12 Sep 2017
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Re: Rectangle ABCD has AB =8 and BC = 6. Point M is the midpoint of diagon  [#permalink]

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12 May 2019, 16:09
Find the area of the triangle, it is a pethagorean triangle 3 - 4 - 5.

Hence, the area is 6.

Because there is not an aswer with 6, the answer must be a multiple of 6.

(A) 65/8 ---> (65*8)/ 6 = Not integer --- Discard
(B) 25/3 ---> (25*3)/ 6 = Not integer --- Discard
(C) 9 ---> Not div by 6 --- Discard
(D) 75/8 ---> (75*8)/ 6 = 100 --- Hold
(E) 85/8 ---> (85*8)/ 6 = Not integer --- Discard

D
Re: Rectangle ABCD has AB =8 and BC = 6. Point M is the midpoint of diagon   [#permalink] 12 May 2019, 16:09
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