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What is the area of right triangle ABC?
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22 Sep 2018, 17:30
22 Sep 2018, 17:30
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What is the area of right triangle ABC?
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Joined: 10 Apr 2015
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Re: What is the area of right triangle ABC?
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20 Dec 2019, 08:17
20 Dec 2019, 08:17
sandy wrote:
While we COULD use the Pythagorean theorem to find the length of side AB (e.g., 12² + x² = 13²), however if we've memorized some Pythagorean triplets, we can solve this question in a matter of seconds.
ASIDE: Pythagorean triplets are integer values that could represent the lengths of a right triangle.
The two most common Pythagorean triples are:
3-4-5
5-12-13
Two more include:
7-24-25
8-15-17
In the above diagram, we can see that we're given two lengths of a 5-12-13 right triangle.
This means side AB = 5
Area of triangle = (base)(height)/2
= (12)(5)/2
= 30
Answer: 30
Cheers,
Brent
Re: What is the area of right triangle ABC?
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11 Jun 2021, 00:26
11 Jun 2021, 00:26
2
30. To find the area of a triangle, a base and height are needed. If the length
of AB can be determined, then AB can be the height and AC can be the base,
because the two sides are perpendicular to each other.
Use the Pythagorean theorem to find the length of side AB: (a)2 + (12)2 =(13)2
, so a2 + 144 = 169, which means that a2 = 25, and finally a = 5.
Alternatively, recognize that the triangle is a Pythagorean triple 5–12–13
Base and height are known, so Area = = 30
of AB can be determined, then AB can be the height and AC can be the base,
because the two sides are perpendicular to each other.
Use the Pythagorean theorem to find the length of side AB: (a)2 + (12)2 =(13)2
, so a2 + 144 = 169, which means that a2 = 25, and finally a = 5.
Alternatively, recognize that the triangle is a Pythagorean triple 5–12–13
Base and height are known, so Area = = 30
