In any triangle the semi-perimeter is greater than each of its sides.

True

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False

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Solution

We know that the sum of two sides of a triangle is
greater than the third side. Hence if a, b, c are the sides
of a triangle, then
$b + c > a$
or $a + b + c > 2 a$ or $\frac{a + b + c}{2} > a$
Similarly $\frac{a + b + c}{2} > b$ and $\frac{a + b + c}{2} > c$

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In any triangle the semi-perimeter is greater than each of its sides.

We know that the sum of two sides of a triangle is greater than the third side. Hence if a, b, c are the sides of a triangle, then b+c>a or a+b+c>2a or a+b+c2>a Similarly a+b+c2>b and a+b+c2>c

We know that the sum of two sides of a triangle is
greater than the third side. Hence if a, b, c are the sides
of a triangle, then
$b + c > a$
or $a + b + c > 2 a$ or $\frac{a + b + c}{2} > a$
Similarly $\frac{a + b + c}{2} > b$ and $\frac{a + b + c}{2} > c$