Can the lengths 7.9 cm, 8.1 cm, and 5.3 cm form a right-angled triangle?
Can the lengths 7.9 centimeters, 8.1 centimeters, and 5.3 centimeters form a right triangle?
In a right triangle, there two shorter sides and a longest side. The longest side is
across from the 90-degree angle. We call it the hypotenuse. Right triangles can use the Pythagorean theorem.
The sum of the squares of the shorter sides is equal to the square of the longest
side. So if we want to know if these three side lengths form a right triangle, we can
use the Pythagorean theorem to decide.
We will plug in 7.9 and 5.3 for the shorter sides and
8.1 for the longest side. So we have 5.3 squared plus 7.9 squared equals 8.1 squared. 5.3 squared is equal to 28.09 and 7.9 squared is equal to 62.41. And finally 8.1 squared is equal to 65.61. Now we
need to add 28.09 and 62.41, which is 90.50, and is that equal to 65.61?
They are not equal. Therefore, these lengths cannot form a right triangle, so our answer is no.
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