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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?

Mathematics
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  • phi
this is more than just ratios. You have to know that opposite sides of a parallelogram are equal. You have 4 sides, |dw:1355358477849:dw| 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 ?
I am trying to graph it and I am the worst
so basically, it would look like this? |dw:1355359130294:dw| and then set them equal to 224 and get x=7 so the side lengths are 63 and 49?

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  • phi
yes that is a nice way to do it
The options are much different

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