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Which of the following statements, considered independently,
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26 Sep 2018, 15:57
26 Sep 2018, 15:57
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Which of the following statements, considered independently, provide sufficient information to calculate the area of triangle ABC?
A. Angle ACB equals 90°
B. AB = 17
C. ABC is a right triangle
Re: Which of the following statements, considered independently,
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11 Jun 2021, 22:36
11 Jun 2021, 22:36
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A,B only.
If angle ACB = 90°, then 8 and
15 are the base and height, and you can calculate the area. The first statement
is sufficient.
If AB = 17, you can plug 8, 15, and 17 into the Pythagorean theorem to see
whether you get a true statement. Use 17 as the hypotenuse in the
Pythagorean theorem because 17 is the longest side:
(8)2 + (15)2 = (17)2
64 + 225 = 289
289 = 289
Since this is true, the triangle is a right triangle with the right angle at C. If
angle ACB = 90°, then 8 and 15 are the base and height, and you can calculate
the area. (Since 8–15–17 is a Pythagorean triple, if you had that fact
memorized, you could skip the step above.) The second statement is
sufficient.
Knowing that ABC is a right triangle (the third statement) is not sufficient to
calculate the area because it’s not specified which angle is the right angle. A
triangle with sides of 8 and 15 could have hypotenuse 17, but another
scenario is possible: perhaps 15 is the hypotenuse. In this case, the third side
is shorter than 15, and the area is smaller than in the 8–15–17 scenario.
If angle ACB = 90°, then 8 and
15 are the base and height, and you can calculate the area. The first statement
is sufficient.
If AB = 17, you can plug 8, 15, and 17 into the Pythagorean theorem to see
whether you get a true statement. Use 17 as the hypotenuse in the
Pythagorean theorem because 17 is the longest side:
(8)2 + (15)2 = (17)2
64 + 225 = 289
289 = 289
Since this is true, the triangle is a right triangle with the right angle at C. If
angle ACB = 90°, then 8 and 15 are the base and height, and you can calculate
the area. (Since 8–15–17 is a Pythagorean triple, if you had that fact
memorized, you could skip the step above.) The second statement is
sufficient.
Knowing that ABC is a right triangle (the third statement) is not sufficient to
calculate the area because it’s not specified which angle is the right angle. A
triangle with sides of 8 and 15 could have hypotenuse 17, but another
scenario is possible: perhaps 15 is the hypotenuse. In this case, the third side
is shorter than 15, and the area is smaller than in the 8–15–17 scenario.
General Discussion
Re: Which of the following statements, considered independently,
[#permalink]
27 Sep 2018, 01:36
27 Sep 2018, 01:36
4
The answer is option A and B because
A) if we are given that angle ACB=90degrees
so, AC becomes the height and BC becomes the base. Using the formula, area=1/2(base*height), we can find the area
B) if we are given the measure of the third side, we can use the heron's formula to calculate the area of the triangle.
C) this statement is not sufficient because we don't know which angle will be 90 degrees and hence can't know which side would be base and which side would be height.
A) if we are given that angle ACB=90degrees
so, AC becomes the height and BC becomes the base. Using the formula, area=1/2(base*height), we can find the area
B) if we are given the measure of the third side, we can use the heron's formula to calculate the area of the triangle.
C) this statement is not sufficient because we don't know which angle will be 90 degrees and hence can't know which side would be base and which side would be height.
