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In the figure above, CBD = BCD . What is the area of triangle A BC?
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04 Jan 2023, 09:23
04 Jan 2023, 09:23
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In the figure above, \(\angle CBD = \angle BCD\) . What is the area of triangle ABC?
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102
Re: In the figure above, CBD = BCD . What is the area of triangle A BC?
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30 Jan 2023, 16:30
30 Jan 2023, 16:30
Expert Reply
OE
The right triangle on the left (triangle ABD) is a 5-12-13 triangle, which is one of the common right triangles with integer side lengths. (Note that you could also use the Pythagorean theorem to determine that the length of BD equals 12: 5^2 + 12^2 = 13^2.) BD is the height of triangle ABC.
Because C B D = B C D , triangle BCD is isosceles, and the length of CD must also equal 12. Thus, the base of triangle A BC has length 5 + 12 = 17, and its area is given by 1/2 bh=1/2 17*12=102
The right triangle on the left (triangle ABD) is a 5-12-13 triangle, which is one of the common right triangles with integer side lengths. (Note that you could also use the Pythagorean theorem to determine that the length of BD equals 12: 5^2 + 12^2 = 13^2.) BD is the height of triangle ABC.
Because C B D = B C D , triangle BCD is isosceles, and the length of CD must also equal 12. Thus, the base of triangle A BC has length 5 + 12 = 17, and its area is given by 1/2 bh=1/2 17*12=102
gmatclubot
Re: In the figure above, CBD = BCD . What is the area of triangle A BC? [#permalink]
30 Jan 2023, 16:30
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