Perimeters

A rectangle has a perimeter of 16p centimeters, it had a width of 2p centimeters. Each side of an equilateral triangle is 1/2 the length of the rectangle. Find the total perimeter of the rectangle and the triangle if p=8.

Correct result:

r =  128 cm
t =  72 cm

Solution:

$$\begin{gathered} p=8 \\ r=16\cdot p=16\cdot 8=128\text{ cm} \end{gathered}$$

$$\begin{gathered} w=2\cdot p=2\cdot 8=16\text{ cm } \\ l=r\mathrm{/}2-w=128\mathrm{/}2-16=48\text{ cm } \\ s={\displaystyle \frac{1}{2}}\cdot l={\displaystyle \frac{1}{2}}\cdot 48=24\text{ cm } \\ t=3\cdot s=3\cdot 24=72\text{ cm} \end{gathered}$$

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