Question

Measures of sides of a triangle are in Arithmetic progression. Its perimeter is $30cm$, and the difference between the longest and shortest side is $4cm$; then find the measures of the sides.

Answer 1

Given, Sides of triangle are in arithmetic progression

Let sides be $(a-d)cms$, $a$ cm and $(a+d)cms$,

Now given perimeter is $30cm$ , that gives $3a=30$ , therefore $a=10cms$.

and also given difference between the longest and shortest side is $4cm$, so $(a+d)-(a-d)=4$, which gives $d=2cms$

Therefore sides of triangle are $8cms$, $10cms$ and $12cms$