Question

can someone please explain to me how to use ratios? i completely forgot and need to know them for a test tomorrow! heres the question- The ratio of 2 consecutive sides of a parallelogram is 7:9. If the perimeter is 224cm, what is the length of the sides?

Answer 1

this is more than just ratios. You have to know that opposite sides of a parallelogram are equal. You have 4 sides,


you also have to know that the perimeter is the distance around the figure, or the sum of lengths of all the sides: a+b+a+b= 2a+2b
2a+2b= perimeter

you now can set this to 224 cm and simplify:
2a+2b= 224 cm
a+b= 112 (divide both sides, all terms by 2)

now you can use the ratio idea
a:b= 7:9 (side a is to side b as 7 is to 9)
or (I like it this way)
\[ \frac{a}{b}= \frac{7}{9} \]

at this point we "solve" for either a or b. Let's solve for "a". multiply both sides by b:
\[ \frac{a}{\cancel{b}}\cdot \cancel{b}= \frac{7b}{9} \]
this says
\[ a= \frac{7b}{9} \]
replace a in your "perimeter equation"
a+b= 112
\[ \frac{7b}{9} + b= 112\]
if we put b over the "common denominator" of 9, we get
\[ \frac{7b}{9}+ \frac{9b}{9}= 112\]
add fractions
\[ \frac{16b}{9}= 112\]
multiply both sides by 9/16, to solve for b
\[ b= \frac{9}{16}\cdot 112\]
after doing the arithmetic you get b=63
can you find a ?

Answer 2

I am trying to graph it and I am the worst

Answer 3

so basically, it would look like this? and then set them equal to 224 and get x=7 so the side lengths are 63 and 49?