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Triangle ABC has perimeter 22cm

AB= 8cm
BC= 5cm
by calculation deduce whether triangle ABC is right-angled triangle

User PriNcee
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1 Answer

9 votes

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Answer:

not a right triangle

Explanation:

The perimeter is 22, so we have ...

AB +BC +CA = 22

8 + 5 + CA = 22

CA = 22 -13 = 9

If this is a right triangle, the sum of the squares of the short sides will be equal to the square of the long side.

AB² +BC² = 8² +5² = 64 +25 = 89

This is not the same as ...

CA² = 9² = 81

The triangle is not a right triangle.

_____

Additional comment

If you're familiar with a few Pythagorean triples, you know that a couple involving a side length 5 are (3, 4, 5) and (5, 12, 13). That is, (5, 8, 9) is NOT a Pythagorean triple, so you know immediately that those side lengths do not form a right triangle. (No calculation is necessary.)

Triangle ABC has perimeter 22cm AB= 8cm BC= 5cm by calculation deduce whether triangle-example-1
User Kalif
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4.3k points