I'm trying to pass my performance task and finish high school and I have no idea what it really is asking me to do, rather how to do it. A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular. The city will pay to have soft pavement made of recycled tires installed in the playground. In the first plan, one side 8 yards longer than the other side. Which equations model the possible dimensions of the playground? x (x - 8) = 256. (x2) - 8 = 256 x (x + 8) = 256. (x + 4) (x - 4) = 256. x2 - 8x - 256 = 0.

Question

Mathematics

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17 December, 04:43

I'm trying to pass my performance task and finish high school and I have no idea what it really is asking me to do, rather how to do it. A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular. The city will pay to have soft pavement made of recycled tires installed in the playground. In the first plan, one side 8 yards longer than the other side. Which equations model the possible dimensions of the playground? x (x - 8) = 256. (x2) - 8 = 256 x (x + 8) = 256. (x + 4) (x - 4) = 256. x2 - 8x - 256 = 0.

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Answers (1)

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Jade Preston · Answer 1

x

8

-

256

Rewrite

x

8

as

(

x

4

)

2

.

(

x

4

)

2

-

256

Rewrite

256

as

16

2

.

(

x

4

)

2

-

16

2

Since both terms are perfect squares, factor using the difference of squares formula,

a

2

-

b

2

=

(

a

+

b

)

(

a

-

b

)

where

a

=

x

4

and

b

=

16

.

(

x

4

+

16

)

(

x

4

-

16

)

Simplify.

Tap for more steps ...

(

x

4

+

16

)

(

x

2

+

4

)

(

x

+

2

)

(

x

-

2

)