What can be concluded about a rectangle's width if the ratio of length to perimeter is 1 to 3? Make some sketches and explain your reasoning.

2 answers

2 L + 2 b = perimeter

L/p = L/(2L+2b) = 1/3

3 L = 2L + 2 b

L = 2 b

the width is half the length
L/P=L/(2W+2L)=1/3. Cross multiply
and solve for W: 2W+2L=3L, 2W=3L-2L,
2W=L, W=L/2. CONCLUSION:The width is
1/2 of the Length.

Sketch a rectangle and L=4, W=2.
L/P SHOULD EQUAL1/3. CHECK:L/(2W+2L)=
4/(4+8)=1/3.