Which value for x would make the perimeter of this rectangle equal 48 inches

L = 16; W=8: are the correct values.

Step-by-step explanation:

Start off with 2 math statements:

First, for the perimeter:  2W x 2L = 48

Then, for the area:  W x L = 128

Next, we want to take the 2nd equation; then solve it for "W"

W x L = 128

Divide out both sides by "L", to get the "W" equals:

W = 128/L

Next, go back to the first equation.  Where it indicates "W", put in the value of:  128/L in its place; to get:

2L + 2*(128/L) = 48; which gives us:

2L + 256/L = 48

Multiply everything by "L", to get:

2L2 + 256 = 48L

Next, divide out everything by 2, to get:

L2 + 128 = 24L

Next, move the 24L over to the left, to get:

L2 - 24L + 128 = 0

(L-16)* (L-8) = 0

L-16 = 0; L-8 = 0

Which gives us:  L=16; L=8

Let's go with the L=16 first; back into the original equation:

f(16) = 2*16 + 2W = 48

32 + 2W = 48

-=32         -32

2W = 16

Divide out both sides by 2, to get:

W = 8

Next, test our values, by plugging them back into both original equations:

2*16 + 2*8 = 48

32 + 16 = 48        [Check]

L x W = 128

16 * 8 = 128

128 = 128          [Check]

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