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What is the area of a quadrilateral with a height of 7, if one side ha

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New post 18 Sep 2018, 22:01
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A
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C
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E

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Question Stats:

49% (01:14) correct 51% (01:10) wrong based on 80 sessions

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What is the area of a quadrilateral with a height of 7, if one side has length 10?

(1) One of the diagonals divides the quadrilateral into two symmetric identical triangles.
(2) The perimeter of the quadrilateral is 42.

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Re: What is the area of a quadrilateral with a height of 7, if one side ha  [#permalink]

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New post 26 Sep 2018, 04:05
Bunuel wrote:
What is the area of a quadrilateral with a height of 7, if one side has length 10?

(1) One of the diagonals divides the quadrilateral into two symmetric identical triangles.
(2) The perimeter of the quadrilateral is 42.


(1) One of the diagonals divides the quadrilateral into two symmetric identical triangles.
Both lengths of a quadrilateral are required for area calculation. This statement does not provide the other length. INSUFFICIENT

(2) The perimeter of the quadrilateral is 42
The other length of the quadrilateral cannot be derived from the perimeter and thus area cannot be calculated. INSUFFICIENT


Answer is E.
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What is the area of a quadrilateral with a height of 7, if one side ha  [#permalink]

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New post 26 Sep 2018, 10:25
Hi !

If the diagnoal divides the quad into symmetric identical triangles
----- the triangles should be congruent
----- perimeter - 20 = 22,
The sum of remaining two sides will be equally divided. Where am i going wrong ?

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Re: What is the area of a quadrilateral with a height of 7, if one side ha  [#permalink]

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New post 30 Sep 2018, 08:28
Can someone pls tell how is the answer E and not C?
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What is the area of a quadrilateral with a height of 7, if one side ha  [#permalink]

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New post 30 Sep 2018, 08:47
helishah142 wrote:
Can someone pls tell how is the answer E and not C?


Acouple of posts above you, I have posted why it is E. Hope that helps helishah142
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What is the area of a quadrilateral with a height of 7, if one side ha  [#permalink]

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New post 30 Sep 2018, 10:18
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Hi ! chetan2u

Thought about this question again. Here is my new interpretation. Please let me know if I am wrong anywhere.
1---- A parallelogram is divided by diagonal into two symmetric (maybe congruent if square) triangles.
So this just tells us that the quadrilateral is some parallelogram. Still we need another side to calculate the area


Am i right with this one (Need a check here). Anyways, ill go on.

2--- By perimeter you cannot ascertain the unique value of base to find out area of triangle.

Combining 1+2,

This parallelogram is some rectangle not a square otherwise perimeter would have been 40.
so 2(x+y) = 42 or x+y = 21 . One of the sides is 10(given), therefore the other side must be 11.
Area = 7*10 or 7*11 we dont know. Therefore insufficient.
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What is the area of a quadrilateral with a height of 7, if one side ha &nbs [#permalink] 30 Sep 2018, 10:18
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