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.

Result

r =  128 cm
t =  72 cm

Solution:

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

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