Question 183
a) In a triangle of sides $a$, $b$ and $c$, it is true whenever the sum of two sides is greater than the third side. For example, in the following triangle, sides $a$, $b$ and $c$, 
is worth the inequality $a \lt b + c$. In addition, two other inequalities are valid. Which are they?
b) In the figure below you can see a rectangle whose smaller side measures 3 and whose larger side measures 8.
Suppose that $a \neq b$. Show that $a + b \gt 10$. Suggestion: Copy a rectangle just like the one drawn on top of it!
c) On each side of a square is chosen a point. Then, these points are linked together to form a quadrilateral, as shown in the figure below:
Shows that the perimeter of this quadrilateral (sum of the lengths of the sides) is greater than or equal to twice the length of the diagonal of the square. Suggestion: Draw several squares equal to the given square!
is worth the inequality $a \lt b + c$. In addition, two other inequalities are valid. Which are they? b) In the figure below you can see a rectangle whose smaller side measures 3 and whose larger side measures 8.
Suppose that $a \neq b$. Show that $a + b \gt 10$. Suggestion: Copy a rectangle just like the one drawn on top of it! c) On each side of a square is chosen a point. Then, these points are linked together to form a quadrilateral, as shown in the figure below:
Shows that the perimeter of this quadrilateral (sum of the lengths of the sides) is greater than or equal to twice the length of the diagonal of the square. Suggestion: Draw several squares equal to the given square!