The ratio of the measures of the sides of a triangle is $3: 4: 6$. If the semiperimeter of the triangle is $39 \, cm$,the measure of the longest side of the triangle is ............ $cm$.

Write True or False and justify your answer.
In a triangle,the sides are given as $11 \, cm$,$12 \, cm$,and $13 \, cm$. The length of the altitude corresponding to the side of length $12 \, cm$ is $10.25 \, cm$.

According to Heron's formula,the area of an equilateral triangle having each side $a$ is ..........

The base of a right triangle is $8 \, cm$ and its hypotenuse is $10 \, cm$. Its area will be (in $cm^2$):

The area of a trapezium is $475 \, cm^2$ and the height is $19 \, cm$. Find the lengths of its two parallel sides if one side is $4 \, cm$ greater than the other.

For an equilateral triangle,each of whose side is $a$,the length of any altitude of that triangle is ...........