Consider the set T of all triangles whose sides are distinct prime numbers which are also in arithmetic progression. Let Δ ∈ T be the triangle with the least perimeter. If a^ is the largest angle of Δ and if L is its

Correct answer: 8 Side must be 3,5,7, ~L=15 aligned & cosa^ =(9+25-49)/(2 × 3 × 5)=-(1)/(2) & a^ =120^ & (a)/(L)=(120)/(15)=8 Ans . aligned

Olympiad workbook

Olympiad workbook · IOQM · Sequences and Series

Consider the set T of all triangles whose sides are distinct prime...

Consider the set T of all triangles whose sides are distinct prime numbers which are also in arithmetic progression. Let

\Delta \in \mathrm{T}

be the triangle with the least perimeter. If

\mathrm{a}^{\circ}

is the largest angle of

\Delta

and if

L

is its perimeter, determine the value of

\frac{a}{L}

Side must be

3,5,7, \quad \mathrm{~L}=15

\begin{aligned} & \operatorname{cosa}^{\circ}=\frac{9+25-49}{2 \times 3 \times 5}=-\frac{1}{2} \\ & a^{\circ}=120^{\circ} \\ & \frac{a}{L}=\frac{120}{15}=8 \text { Ans } . \end{aligned}