Question

Show that the semiperimeter of the triangle is also doubled when each side of the triangle is doubled.

Answer 1

Let us assume a triangle with sides a, b and c.
So, semiperimeter of the triangle= $\frac{a+b+c}{2}$
After doubling the sides, sides will become 2a, 2b and 2c.
So, new semiperimeter = $\frac{2a+2b+2c}{2}=(a+b+c)$, which is twice of the old semiperimeter.
Therefore, the semiperimeter is also doubled.