Question

A book is three times as long as it is wide. Find the length and width of the book in inches if it's area is numerically 128 more than it's perimeter.

Answer 1

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 2

Answer:the width is 8 inches

The length is 24 inches

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