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# The area of triangle is 40. If its height is 2 units more than its bas

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Math Expert
Joined: 02 Sep 2009
Posts: 57279
The area of triangle is 40. If its height is 2 units more than its bas  [#permalink]

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31 Jul 2019, 23:47
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5% (low)

Question Stats:

92% (01:18) correct 8% (02:24) wrong based on 36 sessions

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The area of triangle is 40. If its height is 2 units more than its base, what is the length of its base ?

A. 5
B. 7
C. 8
D. 9
E. 12

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Re: The area of triangle is 40. If its height is 2 units more than its bas  [#permalink]

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31 Jul 2019, 23:52
$$\frac{1}{2}*b*(b+2) = 40$$

$$b^2+2b=80$$

$$b^2+2b-80=0$$

$$(b+10)(b-8)=0$$

$$b=8$$

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Re: The area of triangle is 40. If its height is 2 units more than its bas  [#permalink]

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01 Aug 2019, 00:58
Bunuel wrote:
The area of triangle is 40. If its height is 2 units more than its base, what is the length of its base ?

A. 5
B. 7
C. 8
D. 9
E. 12

Given: The area of triangle is 40. Its height is 2 units more than its base.

Asked: What is the length of its base ?

Let the length of triangle's base be l

Height of triangle = l+2

l(l+2)/2 = 40
l =8; l+2=10; l(l+2)/2 = 40

IMO C
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Re: The area of triangle is 40. If its height is 2 units more than its bas  [#permalink]

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02 Aug 2019, 06:13
The area of a triangle equals to (1/2)*height(h)*the corresponding base(b)
S = (1/2)*h*b =40
h= b + 2
---->(1/2)*(b + 2)*b =40
---->b^2 +2b - 80 =0
We assume that each option is a base of the triangle, so plug in each option by starting from the mid value
b=8--->64 +16 =80--->The answer is B.
We luckily answer the question from the 1st attempt; however, it is recommended to start from the mid value to determine which direction we should choose to check.
---------------------
If the mid value results in:
+Greater value, so we know that we need to move upward. Ex: if our mid value is 9, we have 81 + 18 > 80, so we have to move upward.
+Less value, so we know that we need to move downward. Ex: if our mid value is 7, we have 49 + 14<80, so we have to move downward.
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Re: The area of triangle is 40. If its height is 2 units more than its bas  [#permalink]

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06 Aug 2019, 17:45
Bunuel wrote:
The area of triangle is 40. If its height is 2 units more than its base, what is the length of its base ?

A. 5
B. 7
C. 8
D. 9
E. 12

We can let n = the length of the base and create the equation:

40 = n(n + 2) * 1/2

80 = n^2 + 2n

n^2 + 2n - 80 = 0

(n + 10)(n - 8) = 0

n = -10 or n = 8

Since n can’t be negative, n must be 8.

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Re: The area of triangle is 40. If its height is 2 units more than its bas   [#permalink] 06 Aug 2019, 17:45
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