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In right triangle ABC above, side AB has a length of x units, side AC

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Bunuel
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In right triangle ABC above, side AB has a length of x units, side AC [#permalink] New post   03 Jan 2019, 13:12
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In right triangle ABC above, side AB has a length of x units, side AC has a length of 12 units, and side BC has a length of x + 8 units. What is the area of ABC in square units?

A. 25
B. 28
C. 29
D. 30
E. 32

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D
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MahmoudFawzy
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Re: In right triangle ABC above, side AB has a length of x units, side AC [#permalink] New post   03 Jan 2019, 15:12
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Bunuel wrote:

In right triangle ABC above, side AB has a length of x units, side AC has a length of 12 units, and side BC has a length of x + 8 units. What is the area of ABC in square units?

A. 25
B. 28
C. 29
D. 30
E. 32

Show Spoiler
Attachment:
triangle.jpg


according to Pythagoras:
\(x^2 + 12^2 = (x+8)^2\)
\(x^2 + 144 = x^2 + 16x + 64\)
16x = 80
x = 5

the area = \(\frac{5*12}{2}\) = 30

so D
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In right triangle ABC above, side AB has a length of x units, side AC [#permalink] New post   03 Jan 2019, 15:23
Area = 1/2 x AC x AB = 1/2 x 12 x x =6x

Answer is a multiple of 6 ====> Answer D is the only multiple of 6 and thus the correct answer.


Bunuel wrote:

In right triangle ABC above, side AB has a length of x units, side AC has a length of 12 units, and side BC has a length of x + 8 units. What is the area of ABC in square units?

A. 25
B. 28
C. 29
D. 30
E. 32

Show Spoiler
Attachment:
triangle.jpg
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MahmoudFawzy
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Re: In right triangle ABC above, side AB has a length of x units, side AC [#permalink] New post   03 Jan 2019, 15:36
funsogu wrote:
Area = 1/2 x AC x AB = 1/2 x 12 x x =6x

Answer is a multiple of 6 ====> Answer D is the only multiple of 6 and thus the correct answer.



take care that your thesis relies on the assumption that x must be an integer, which is not stated in the question.
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Re: In right triangle ABC above, side AB has a length of x units, side AC [#permalink] New post   03 Jan 2019, 15:39
Mahmoudfawzy83 True. Thanks for the observation.


Mahmoudfawzy83 wrote:
funsogu wrote:
Area = 1/2 x AC x AB = 1/2 x 12 x x =6x

Answer is a multiple of 6 ====> Answer D is the only multiple of 6 and thus the correct answer.



take care that your thesis relies on the assumption that x must be an integer, which is not stated in the question.
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In right triangle ABC above, side AB has a length of x units, side AC [#permalink] New post   04 Jan 2019, 03:39
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Solution


Given:
ABC is a right-angled triangle at A
    • AB = x units
    • AC = 12 units
    • BC = x + 8 units

To find:
    • The area of ABC in sq. units

Approach and Working:
\(AC^2 + AB^2 = BC^2\)
    • \(12^2 + x^2 = (x + 8)^2\)
    • 16x = 144 – 64
    • Thus, x = 5

Therefore, area of ABC = \(\frac{1}{2} * AC * AB = \frac{1}{2} * 12 * 5 = 30\)

Hence, the correct answer is Option D

Answer: D

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Re: In right triangle ABC above, side AB has a length of x units, side AC [#permalink] New post   06 Jan 2019, 06:17
Bunuel wrote:

In right triangle ABC above, side AB has a length of x units, side AC has a length of 12 units, and side BC has a length of x + 8 units. What is the area of ABC in square units?

A. 25
B. 28
C. 29
D. 30
E. 32

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Attachment:
triangle.jpg


solve for x

we get x = 5

area = 0.5*5*12= 30

IMO D
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Re: In right triangle ABC above, side AB has a length of x units, side AC [#permalink]
06 Jan 2019, 06:17
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