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 answer:

r =  128 cm
t =  72 cm

Step-by-step explanation:

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

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

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