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# If the area of the right triangle above is 18, what is the value of x?

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Math Expert
Joined: 02 Sep 2009
Posts: 47112
If the area of the right triangle above is 18, what is the value of x?  [#permalink]

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01 Sep 2017, 07:39
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5% (low)

Question Stats:

81% (00:36) correct 19% (00:31) wrong based on 81 sessions

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If the area of the right triangle above is 18, what is the value of x?

(A) 60
(B) 50
(C) 45
(D) 30
(E) cannot be determined

Attachment:

2017-09-01_1836.png [ 9.91 KiB | Viewed 1045 times ]

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Re: If the area of the right triangle above is 18, what is the value of x?  [#permalink]

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01 Sep 2017, 07:49
Bunuel wrote:

If the area of the right triangle above is 18, what is the value of x?

(A) 60
(B) 50
(C) 45
(D) 30
(E) cannot be determined

Attachment:
2017-09-01_1836.png

Length of height $$= 6$$

Let the length of base be $$= a$$

Area $$= \frac{1}{2} * base *height = \frac{1}{2} * 6 * a = 18$$

$$3a = 18$$

$$a = \frac{18}{3} = 6$$

Therefore its isosceles right triangle.

$$x = 45$$

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If the area of the right triangle above is 18, what is the value of x?  [#permalink]

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01 Sep 2017, 14:59
Similarly, the problem can be solved through trigonometry:
Given that tg(alpha)= (cathetus #1 / cathetus #2), and, given that the unknown cathetus of this triangle can be computed via the above suggested method, we are settled down to observe that (cathetus #1 / cathetus #2), in fact, obtains the value of 1. The direct implication of this derivation is - guess what? - the value of the angle of our concern - 45 degrees.

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Re: If the area of the right triangle above is 18, what is the value of x?  [#permalink]

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07 Sep 2017, 13:59
In right angle triangle , perpendicular is 6 and Area of triangle is 18.

thus , 1/2 * B * H = 18
B = 6

As two sides of triangle are equal , it is known as right isosceles triangle.
Now, the value of x = 45

Option : C
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Re: If the area of the right triangle above is 18, what is the value of x?  [#permalink]

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12 Sep 2017, 02:05
Hi, I appreciate your help with the following:

The question asks regarding the value of x when the triangle's area is above 18 (i.e., when x > 6 because when a question says Area > 18 this means that 1/2 x b x h > 18 = 1/2 x b x 6 > 18 = 1/2 b > 3 -> b > 6) therefore the area is 18 and not above. I frankly don't quite get the point here?!
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Re: If the area of the right triangle above is 18, what is the value of x?  [#permalink]

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12 Sep 2017, 02:14
Rabz wrote:
Hi, I appreciate your help with the following:

The question asks regarding the value of x when the triangle's area is above 18 (i.e., when x > 6 because when a question says Area > 18 this means that 1/2 x b x h > 18 = 1/2 x b x 6 > 18 = 1/2 b > 3 -> b > 6) therefore the area is 18 and not above. I frankly don't quite get the point here?!

"Above" here does not mean "more than", it refers to the triangle which is above the text.
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Re: If the area of the right triangle above is 18, what is the value of x?  [#permalink]

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12 Sep 2017, 03:29
Given a rt angle triangle : Area = 1/2 * 6 * base = 18 -----> Base = 6
tan x = 6/6 ----> x = tan-1(1) ----> x= 45
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Re: If the area of the right triangle above is 18, what is the value of x?  [#permalink]

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15 Sep 2017, 10:13
Bunuel wrote:

If the area of the right triangle above is 18, what is the value of x?

(A) 60
(B) 50
(C) 45
(D) 30
(E) cannot be determined

Recall that the formula for the area of a triangle is A = bh/2. We can let b = the base of the triangle and create the following equation:

(6 x b)/2 = 18

6b = 36

b = 6

We see that the triangle is an isosceles right triangle. Since x is the measure of an acute angle of an isosceles right triangle, it must be 45.

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Re: If the area of the right triangle above is 18, what is the value of x?  [#permalink]

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15 Sep 2017, 10:58
1/2 Base * Height is the area of the triangle.

-- 6 (height) * 3 (half the base) = 18 so the base is 6

If two sides of a right triangle are equal, their angles must correspond with 45, 45, 90. Hence, the right answer is (C), 45 degrees.
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