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Joined: 10 Dec 2020
Posts: 50
Given Kudos: 955
GRE 1: Q166 V162
In the figure above, square ACBD has an area of 9 and square DEFG has
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Updated on: 29 Nov 2021, 07:21
Updated on: 29 Nov 2021, 07:21
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In the figure above, square ACBD has an area of 9 and square DEFG has an area of 16.
Quantity A |
Quantity B |
The area of triangle BED |
8 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Originally posted by XavierAlexander on 29 Nov 2021, 06:52.
Last edited by XavierAlexander on 29 Nov 2021, 07:21, edited 1 time in total.
Last edited by XavierAlexander on 29 Nov 2021, 07:21, edited 1 time in total.
Manager
Joined: 10 Dec 2020
Posts: 50
Given Kudos: 955
GRE 1: Q166 V162
Re: In the figure above, square ACBD has an area of 9 and square DEFG has
[#permalink]
29 Nov 2021, 06:55
29 Nov 2021, 06:55
1
Official explanation from MGRE:
If the area of square ACBD is 9, then its sides each have length 3. If the area of square DEFG is 16, then its sides each have length 4. Specifically, two of the sides of the triangle (BD and DE) have lengths 3 and 4, respectively.
The area of a triangle is ½ bh, and is the same regardless of which side is used as the base. So, use DE = 4 as the base of the triangle. If this side is the base, then the height is as shown:
Using side DE as the base, the height must be no greater than 3, since it cannot be longer than the sides of the triangle. (The greatest possible value for the height is exactly 3, which will only be the case if the triangle is a right triangle.) Therefore, the area must be no greater than ½(3)(4) = 6. So, Quantity B is always greater.
The correct answer is B.
If the area of square ACBD is 9, then its sides each have length 3. If the area of square DEFG is 16, then its sides each have length 4. Specifically, two of the sides of the triangle (BD and DE) have lengths 3 and 4, respectively.
The area of a triangle is ½ bh, and is the same regardless of which side is used as the base. So, use DE = 4 as the base of the triangle. If this side is the base, then the height is as shown:
Using side DE as the base, the height must be no greater than 3, since it cannot be longer than the sides of the triangle. (The greatest possible value for the height is exactly 3, which will only be the case if the triangle is a right triangle.) Therefore, the area must be no greater than ½(3)(4) = 6. So, Quantity B is always greater.
The correct answer is B.
Re: In the figure above, square ACBD has an area of 9 and square DEFG has
[#permalink]
29 Nov 2021, 07:10
29 Nov 2021, 07:10
1
Thank you for the interesting Geometry problem. I panicked for a moment because in the answer box it says *A* is the correct answer. But it's actually B right?
