It is given in the question that ,
Anja is creating a triangle using three straws. The two shorter straws have lengths of 20 cm and 21 cm. How long, in centimeters.
Let the third side, which is the hypotenuse is c .
Now we use the pythagorean identity, which is
[tex]a^2 + b^2 = c^2[/tex]
where a and b are the legs .
Substituting the given values of the two legs, we will get
[tex]20^2 + 21^2 = c^2 \\ 400 +441= c^2 \\ c^2 = 841 \\ c = \sqrt{841} \\ c =29cm[/tex]
So the length of third side have to be 29 cm .
Answer: The length of the third straw is 29 centimeters.
Step-by-step explanation: Given that Anja is creating a triangle using three straws and the lengths of two shorter straws are 20 cm and 21 cm.
We are to find the length of the third straw in centimeters so that Anja will create a right triangle.
The two shorter straws will make the legs of the right-angled triangle because they are shorter.
Since the third straw will be the largest, so it will make the HYPOTENUSE of the triangle.
In a right-angled triangle, we have
Hypotenuse² = length of one leg² + length of the other leg².
Therefore, we get
[tex]Hypotenuse^2=20^2+21^2=400+441=841\\\\\Rightarrow Hypotenuse=29.[/tex]
Thus, the length of the third straw is 29 centimeters.