Buddy is going to decorate his rectangular backyard with holiday lights. The area of his backyard is 72 square feet and the perimeter is 34 feet. If he wants to use one color for the widths and another color for the lengths, how long does each color on each side need to be to cover the entire perimeter of his backyard?

The length of the color of each side has to be 9 ft long and 8 ft wide or 8 ft long and 9 ft wide for it to be able to cover the entire perimeter of the wall.

Step-by-step explanation:

Let l be the length of the wall and b its breadth. Its area A = lb = 72 ft² (1)

Also, its perimeter P = 2(l + b) = 34 ft  

l + b = 17 (2)

From equation (1),

l = 72/b

substituting this into (2), we have

72/b + b = 17

multiplying through by b, we have

72 + b² = 17b

simplifying, we have

b² - 17b + 72 = 0

We find b by factorizing

So, b² - 8b - 9b + 72 = 0

b(b - 8) -9(b - 8) = 0

(b - 8)(b - 9) = 0

b - 8 = 0 or b - 9 =0

b = 8 or b = 9

Substituting b = 8 into l, we have

l = 72/b = 72/8 = 9

Substituting b = 9 into l, we have

l = 72/b = 72/9 = 8

So, the length of the color of each side has to be 9 ft long  and 8 ft wide or 8 ft long and 9 ft wide for it to be able to cover the entire perimeter of the wall.

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional