Answer:
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]
