Question

Topic(s): UPPER AND LOWER BOUND
An equilateral triangle has sides of length 16.1 cm, correct to the nearest millimetre.
Find the lower and upper bounds of the perimeter of the triangle.

Answer 1

Resposta:

Explicação passo a passo:

We can take $\varepsilon = 0.05$ to get upper and lower bounds. So, we know that equilateral triangle has all sides with the same length ($\ell$), then the perimeter ($p$) is $3 \ell$.  

If $\ell = 16.1\ \si{cm}$, lower bound is $\ell - \varepsilon = 16.05\ \si{cm}$ and upper bound is $\ell + \varepsilon = 16.15\ \si{cm}$.

So the lower bound of perimeter is $3\times (\ell - \varepsilon) = 3 \times 16.05\ \si{cm} = 48.15\ \si{cm}$ and the upper bound of perimeter is $3\times (\ell + \varepsilon) = 3\times 16.15\ \si{cm} = 48.45\ \si{cm}$