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# If h and b represent the height and base, respectively, of the triangl

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Math Expert
Joined: 02 Sep 2009
Posts: 60460
If h and b represent the height and base, respectively, of the triangl  [#permalink]

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07 Sep 2018, 00:55
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Difficulty:

55% (hard)

Question Stats:

60% (01:30) correct 40% (01:52) wrong based on 104 sessions

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If h and b represent the height and base, respectively, of the triangle above, what is the perimeter of the triangle?

(A) Three times the base is 3 more than the height.
(B) The average of the base and height is 8.5.

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image001.jpg [ 2.11 KiB | Viewed 1031 times ]

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Re: If h and b represent the height and base, respectively, of the triangl  [#permalink]

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07 Sep 2018, 02:15
Bunuel wrote:

If h and b represent the height and base, respectively, of the triangle above, what is the perimeter of the triangle?

(A) Three times the base is 3 more than the height.
(B) The average of the base and height is 8.5.

Attachment:
image001.jpg

Question : what is the perimeter of the triangle?

Statement 1: Three times the base is 3 more than the height.

3b = 3+h
but we need one more equation to calculate the values of base and heights along with the third side of this right triangle

P.S. The given triangle is a right triangle because base and height of a triangle are always perpendicular to each other

Not sufficient

Statement 2: The average of the base and height is 8.5.

i.e. b+h = 8.5*2 = 17

but we need one more equation to calculate the values of base and heights along with the third side of this right triangle

NOT SUFFICIENT

Combining the two statetements

we have two equations and two variables so base and height can be calculated and afterwards teh hypotenuse as well hence

SUFFICIENT

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Re: If h and b represent the height and base, respectively, of the triangl  [#permalink]

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19 Sep 2018, 01:12
1
Right trianlge? Its nowhere mentioned in the question that the triangle is a right angled triangle
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Re: If h and b represent the height and base, respectively, of the triangl  [#permalink]

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07 Dec 2019, 00:38
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sahil
Yes! it is true that the problem did not mention that triangle is a`right`triangle but the problem did mention that `h` is the height! And a height is perpendicular to base and creates two 90 degree angles; this properties is sufficient to say that we are dealing with a `right` triangle.
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If h and b represent the height and base, respectively, of the triangl  [#permalink]

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10 Dec 2019, 23:04
Side Vs Height

Rather than 2 sides, they say height and base, for any triangle height is 90degrees to the base.
so, we will be able to find the Hyp and hence the perimeter.

So C.

(But if these were sides, it will be E.)
If h and b represent the height and base, respectively, of the triangl   [#permalink] 10 Dec 2019, 23:04
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