Respuesta :
Answer:
Step-by-step explanation:
let width=w
length=l
l=3w
P=2(l+w)=2(3w+w)=8w
A=l*w=3w*w=3w²
3w²=8w+128
3w²-8w-128=0
3w²-24w+16w-128=0
3w(w-8)+16(w-8)=0
(w-8)(3w+16)=0
w=8,-16/3 (rejected)
width=8
length=8*3=24
Answer:the width is 8 inches
The length is 24 inches
Step-by-step explanation:
Let L represent the length of the book.
Let W represent the width of the book.
A book is three times as long as it is wide. This means that
L = 3W
if it's area is numerically 128 more than it's perimeter. It means that
LW - 128 = 2(L + W) - - -- - - - - - 1
Substituting L = 3W into equation 1, it becomes
3W × W - 128 = 2(3W + W)
3W^2 - 128 = 8W
3W^2 - 8W - 128 = 0
3W^2 + 16W - 24W - 128 = 0
W(3W + 16) - 8(3W + 16) = 0
(W - 8)(3W + 16) = 0
W - 8 = 0 or 3W + 16 = 0
W = 8 or W = - 16/3
Since the width of the book cannot be negative, then W = 8 inches
Substituting W = 8 into L = 3W, it becomes
L = 3 × 8 = 24 inches
