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25 Mar 2022, 01:30
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D
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Difficulty:
45%
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Question Stats:
58% (01:13) correct
42%
(01:01)
wrong
based on 67
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Is ΔABC an isosceles triangle?
(1) AD = DC
(2) The area of ΔABD equals the area of ΔBDC
Attachment:
GMAT_DS_Magoosh_168.png [ 2.52 KiB | Viewed 2173 times ]
25 Mar 2022, 02:55
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1) As AD = DC, let their lengths be x. Using Pythagoras to solve the respective hypotenuses of the two triangles we find that:
△ABD: \(x^2+BD^2 = AB^2\)
△CBD: \(x^2+BD^2 = BC^2\)
Looking at the two equations we can see that \(AB^2 = BC^2\) and like wise that \(AB = BC\) making △ABC an isosceles triangle.
SUFFICIENT
2) As the area of ΔABD equals the area of ΔBDC, and they share a common height we can deduce that the length of the respective bases has to be the same given that the formula for the area of a triangle is: \(\frac{Base * Height}{2}\), which means once again that if we use Pythagoras to solve for the respective hypotenuses as done in 1), we will find that they are equal. Which means that △ABC is isosceles
SUFFICIENT
Answer D
△ABD: \(x^2+BD^2 = AB^2\)
△CBD: \(x^2+BD^2 = BC^2\)
Looking at the two equations we can see that \(AB^2 = BC^2\) and like wise that \(AB = BC\) making △ABC an isosceles triangle.
SUFFICIENT
2) As the area of ΔABD equals the area of ΔBDC, and they share a common height we can deduce that the length of the respective bases has to be the same given that the formula for the area of a triangle is: \(\frac{Base * Height}{2}\), which means once again that if we use Pythagoras to solve for the respective hypotenuses as done in 1), we will find that they are equal. Which means that △ABC is isosceles
SUFFICIENT
Answer D
