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2 years ago

Can you have a right triangle where the lengths of the legs are whole numbers and the length of the hypotenuse is 23? Explain.

Mathematics

2 answers:

dezoksy [38]2 years ago

7 0

No you can't because a right angle is 90

Norma-Jean [14]2 years ago

3 0

Answer: No,it is not possible to have a right triangle where the lengths of the legs are whole numbers and the length of the hypotenuse is 23.

Step-by-step explanation:

According to the Pythagorean triplet, in a right angled triangle the hypotenuse is the longest side.

and it is given by $m^2+1$ and other two legs are given by $m^2-1$ and $2m$

Now, the longest side= $m^2+1=23$

$\Rightarrow\ m^2=23-1\\\Rightarrow\ m^2=22$

But 22 is not a perfect square

Since $4^2=16$ and $5^2=25$ , therefore the square root of 22 lies between 4 and 5.

Hence, it is not possible to have a right triangle where the lengths of the legs are whole numbers and the length of the hypotenuse is 23.

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Since we need to base the solutions of the system on one of the independent terms ( $h$ ), the determinant method is not suitable and therefore we use the Gauss elimination method.

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