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

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Math Expert
Joined: 02 Sep 2009
Posts: 57087
In right triangle ABC above, side AB has a length of x units, side AC  [#permalink]

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03 Jan 2019, 13:12
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Difficulty:

5% (low)

Question Stats:

92% (01:12) correct 8% (03:40) wrong based on 50 sessions

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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

Attachment:

triangle.jpg [ 11.71 KiB | Viewed 669 times ]

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Re: In right triangle ABC above, side AB has a length of x units, side AC  [#permalink]

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03 Jan 2019, 15:12
1
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

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]

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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

Attachment:
triangle.jpg
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Re: In right triangle ABC above, side AB has a length of x units, side AC  [#permalink]

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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]

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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]

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04 Jan 2019, 03:39

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

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Re: In right triangle ABC above, side AB has a length of x units, side AC  [#permalink]

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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

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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