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## Sagot :

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.**