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# In a triangle ABC where ∠B is a right angle:

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Manager
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Joined: 27 Oct 2018
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In a triangle ABC where ∠B is a right angle:  [#permalink]

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03 Jan 2019, 15:29
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00:00

Difficulty:

55% (hard)

Question Stats:

62% (02:55) correct 38% (02:22) wrong based on 28 sessions

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In a triangle ABC where ∠B is a right angle: 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. 10
B. 15
C. 16.5
D. 20
E. 22

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Re: In a triangle ABC where ∠B is a right angle:  [#permalink]

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03 Jan 2019, 19:50
2
Mahmoudfawzy83 wrote:
In a triangle ABC where ∠B is a right angle: 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. 10
B. 15
C. 16.5
D. 20
E. 22

So angle B is 90, so the side opposite to it, AC is hypotenuse..
With sides x, x+8 and 12...
$$x^2+(x+8)^2=12^2......x^2+x^2+16x+64=144.......x^2+8x=40.....x (x+8)=40$$

The area of this triangle is $$\frac{1}{2}*x(x+8)=\frac{40}{2}=20$$

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Re: In a triangle ABC where ∠B is a right angle:   [#permalink] 03 Jan 2019, 19:50
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