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16 Oct 2022, 23:05
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
61% (02:57) correct
39%
(02:31)
wrong
based on 28
sessions
History
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Attachment:
da376cef0083b1572fb9fe933bd36903.jpg [ 7.56 KiB | Viewed 1731 times ]
A. \( \frac{6}{9}\)
B. \(\frac{ 5}{9}\)
C. \(\frac{8}{9}\)
D. \( \frac{1}{2}\)
E. \( \frac{1}{3}\)
17 Oct 2022, 07:16
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Afroditee
Take \(\triangle ADE\) and \(\triangle ABC\)
The sides are in ratio 1:3, so the area will be in ratio \(1^2:3^2\) or 1:9.
Now take \(\triangle CEF\) and \(\triangle CAB\)
The sides are in ratio 2:3, so the area will be in ratio \(2^2:3^2\) or 4:9.
Area of shaded portion : Area of the entire triangle
(1+4):9 or 5:9
B
17 Oct 2022, 17:29
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A non standard GMAT approach:
The Area of a triangle can be found if you know the values of S-A-S, two adjacent side lengths and the measure of the included angle.
Area of a Triangle = (1/2) (a) (b) (SINE Included Angle)
For this problem, we do not have to know the value of the included Angle. We can use the formula to find the ratio of the triangle areas.
(1st) Ratio of Area of lower left triangle ADE to the entire triangle using Angle <A
The Area of ADE, in “ratio units”, would be:
(1/2) (1x) (1a) (Sine <A)
The Area of the entire triangle:
(1/2) (3x) (3a) (Sin <A)
Divide the two expressions and we get the ratio:
(area of triangle ADE) / (area of triangle ABC) =
(1/2) (1x) (1a) (Sin <A)
_______________________
(1/2) (3x) (3a) (Sin <A)
= 1/9
Triangle ADE represents 1/9 of the triangle
(2nd) same calculations with respect to triangle EFC and the entire triangle AND using the included Angle at vertex C
(1/2) (2z) (2a) (Sine Angle <C)
_______________________________
(1/2) (3z) (3a) (Sine Angle <C)
= 4 / 9
Area of triangle EFC is (4/9) of the area of the entire triangle
(1/9) + (4/9) =
5/9
*B*
Posted from my mobile device
The Area of a triangle can be found if you know the values of S-A-S, two adjacent side lengths and the measure of the included angle.
Area of a Triangle = (1/2) (a) (b) (SINE Included Angle)
For this problem, we do not have to know the value of the included Angle. We can use the formula to find the ratio of the triangle areas.
(1st) Ratio of Area of lower left triangle ADE to the entire triangle using Angle <A
The Area of ADE, in “ratio units”, would be:
(1/2) (1x) (1a) (Sine <A)
The Area of the entire triangle:
(1/2) (3x) (3a) (Sin <A)
Divide the two expressions and we get the ratio:
(area of triangle ADE) / (area of triangle ABC) =
(1/2) (1x) (1a) (Sin <A)
_______________________
(1/2) (3x) (3a) (Sin <A)
= 1/9
Triangle ADE represents 1/9 of the triangle
(2nd) same calculations with respect to triangle EFC and the entire triangle AND using the included Angle at vertex C
(1/2) (2z) (2a) (Sine Angle <C)
_______________________________
(1/2) (3z) (3a) (Sine Angle <C)
= 4 / 9
Area of triangle EFC is (4/9) of the area of the entire triangle
(1/9) + (4/9) =
5/9
*B*
Posted from my mobile device
