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

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In right triangle ABC above, side AB has a length of x units [#permalink] New post   21 Oct 2018, 08:38
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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?

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Re: In right triangle ABC above, side AB has a length of x units [#permalink] New post   21 Oct 2018, 19:33
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Carcass wrote:
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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?

Show: :: square units
30



To find the area of the right-angled triangle, the height "x" is required.

As per the information,

122+x2=(x+8)2

or 144+x2=x2+16x+64

or x=5
Area of triangle = 12∗AC(base)∗Height(AB)=12∗12∗5=30
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In right triangle ABC above, side AB has a length of x units [#permalink] New post   16 Mar 2019, 00:42
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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?

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Re: In right triangle ABC above, side AB has a length of x units [#permalink] New post   20 Mar 2019, 16:30
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First we have to solve for x. Using the Pythagorean theorem:

x² + 12² = (x + 8)²

Expand the right:

x² + 12² = x² + 16x + 64

Subtract x² from both sides:

12² = 16x + 64

Subtract 64:

12² - 64 = 16x

Simplify:

80 = 16x

Divide by 16:

x = 5

If x = 5, then AB = 5 and AC = 12. If we use AB as the base, then AC is the height, and the area is one half of the base times the height. 5*12 = 60, and one half of that is 30. So the area of the triangle is 30.
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Re: In right triangle ABC above, side AB has a length of x units [#permalink] New post   01 Apr 2021, 03:38
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Re: In right triangle ABC above, side AB has a length of x units [#permalink] New post   06 Jan 2022, 09:37
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Re: In right triangle ABC above, side AB has a length of x units [#permalink]
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