Question

. In two similar parallelograms, the sides of the first parallelogram to the sides of the second parallelogram are in the ratio of 3:2. What is the ratio of their perimeters?
A. 3:2
B. 9:4
C. 27:8
D. none of the above

Answer 1

Now the ratio of the sides is given by:\[\bf \frac{ x }{ m }=\frac{ y }{ n }=\frac{ 3 }{ 2 }\]The perimeter for the parallelogram with sides 'x' and 'y' is:\[\bf P_1=2x+2y=2(x+y)\]The perimeter for the second parallelogram with sides 'm' and 'n' is:\[\bf P_2=2m+2n=2(m+n)\]When we take the ratio of P1 and P2, we get:\[\bf \frac{ P_1 }{ P_2 }=\frac{ \cancel2(x+y) }{ \cancel2(m+n) }=\frac{ x+y }{ m+n }\]From the ratios we started with we derive the following:\[\bf \frac{x}{m}=\frac{3}{2} \implies x=\frac{3}{2}m\]\[\bf \frac{y}{n}=\frac{3}{2}\implies y=\frac{3}{2}n\]Plugging in these values for 'b' and 'y' in to our P1/P2 equation, we get:\[\bf \frac{ P_1 }{ P_2 }= \frac{x+y}{m+n}=\frac{ \frac{ 3 }{ 2 }m+\frac{ 3 }{ 2 }n }{ m+n }=\frac{ 3 }{ 2 }\left( \frac{ m+n }{ m+n } \right)=\frac{ 3 }{ 2 }\]Hence the ratio of the perimeters is 3/2.

@Ambbiiee

Answer 2

@Ambbiiee

Answer 3

u there?

Answer 4

yeah i am reading it

Answer 5

should i just plug it in

Answer 6

After you substitute 3/2m and 3/2n in to the p1/p2 perimeter ratio for x and y, you then factor out the 3/2. (m+n)/(m+n) is just 1 so that cancels and we are left with just 3/2. So the ratio of the perimeters is also 3/2. @ambbiiee