Review question

# Can we prove that, for a triangle, $4(s-b)(s-c) \le a^2$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8056

## Question

The sides of a triangle are $a$, $b$, $c$, and $s$ is given by $2s = a + b + c$.

Prove that

1. $4(s-b)(s-c) \le a^2$,
2. $8(s-a)(s-b)(s-c) \le abc$.

State under what conditions the sign of equality applies, in each case.

Investigate the truth of the results (i) and (ii) if $a$, $b$, $c$ are any positive quantities, not necessarily the sides of a triangle.