MCQ
In which of the following cases, a right triangle cannot be constructed?
- ✓$12\ cm, 5\ cm, 13\ cm$
- B$8\ cm, 6\ cm, 10\ cm$
- C$5\ cm, 9\ cm, 11\ cm$
- DNone of these.
✓
Answer
Correct option: A.
$12\ cm, 5\ cm, 13\ cm$
In $(a)$
$12^2 + 5^2 = 13^2$
$\Rightarrow 144 + 25 = 169$
$\Rightarrow 169$
Since, the sum of the square of two smallest side is equal to the square of largest side.
Hence, a right triangle can be constructed.
In $(b)$
$8^2 + 6^2 = 10^2$
$\Rightarrow 44 + 36 = 100$
$\Rightarrow 100 = 100$
Since, the sum of the square of two smallest side is equal to the square of largest side.
Hence, a right triangle can be constructed.
In $(c)$
$5^2+9^2\neq11^2$
$\Rightarrow 25+81\neq121$
$\Rightarrow 106\neq121$
Since, the sum of the square of two smallest side is not equal to the square of largest side.
Hence, a right triangle can not be constructed.
Hence, the correct answer is option $(a).$
$12^2 + 5^2 = 13^2$
$\Rightarrow 144 + 25 = 169$
$\Rightarrow 169$
Since, the sum of the square of two smallest side is equal to the square of largest side.
Hence, a right triangle can be constructed.
In $(b)$
$8^2 + 6^2 = 10^2$
$\Rightarrow 44 + 36 = 100$
$\Rightarrow 100 = 100$
Since, the sum of the square of two smallest side is equal to the square of largest side.
Hence, a right triangle can be constructed.
In $(c)$
$5^2+9^2\neq11^2$
$\Rightarrow 25+81\neq121$
$\Rightarrow 106\neq121$
Since, the sum of the square of two smallest side is not equal to the square of largest side.
Hence, a right triangle can not be constructed.
Hence, the correct answer is option $(a).$
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