Triangles' Triangle
The perimeter of a large triangle is 24 cm. What is the total length of the black lines used to draw the figure?
The perimeter of the large triangle is 24 cm. What is the total length of the black lines used to draw the figure?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
The perimeter of the large triangle is $24 \; \text{cm}$, so it has side of length $8 \; \text{cm}$, so each small triangle has side of length $1 \; \text{cm}$. So each small triangle has perimeter $3 \; \text{cm}$
\begin{eqnarray}\text{Total length of black lines} &=& \text{Total perimeter of shaded triangles} \\ &=& \text{Number of shaded triangles} \times 3\; \text{cm} \\ &=& 27 \times 3\; \text{cm}\\ &=& 81\; \text{cm} \end{eqnarray}