An envelope is 4 cm longer than it is wide. The area is 96 cm squared. Find the length and width.?

Question

Show work (explain)
Thanks

Answer 1

L = W + 4

Area = L * W

Area = (W + 4) * W

Area = W^2 + 4W

96 = W^2 + 4W

Two roots: 8 and -12.

Let's rule out the negative value, and have width 8 cm.
Therefore Length is 8 + 4 = 12

And 8 * 12 is indeed 96.

Answer 2

Area = length x width

Let a = width of envelope

Then a + 4 = length

96 = a*(a+4)

a^2 +4a = 96

a^2 +4a -96 = 0

(a-8)(a+12) = 0

a = 8 cm width

a +4 = 12 cm length

You will note that the quadratic equation also had a negative solution of 12. This is a trivial solution because a dimension cannot be negative.
.

Answer 3

L = length ; W = Width ; A = area A = WL A = seventy seven L = W + 4 seventy seven = W (W + 4) seventy seven = W^2 + 4W - finished the sq.: Divide 4 in a million/2, then squared, upload answer to the two factors seventy seven + 4 = W^2 + 4W + 4 80 one = (W + 2)^2 - sq. root the two factors W + 2 = Sqrt of 80 one - The Sqrt of 80 one is 9 AND -9 W + 2 = 9 AND W + 2 = -9 answer :: W = 7 AND W = -eleven No such project as damaging width/measurement. pass out W = -eleven L = 7 + 4 = eleven very final answer :: W = 7 ; L = eleven

Answer 4

it has rectangular shape so it is area is base*height
base (length) = x
height (width) = x-4 (because 4 cm less than length)
so x*(x-4)= 96 cmsq
x^2-4x-96=0 >
length = x=12 cm (the positive root because length can't be negative)
and width = x-4= 12-4= 8 cm
check: 12*8= 96 cmsq

Answer 5

L = 4 + w

Lw = 96

(w)(4 + w) = 96

4w + w^2 = 96

w^2 + 4w - 96 = 0

(w + 12)(w - 8) = 0

w + 12 = 0

w = -12

(toss out this answer, width can't be negative)

w - 8 = 0

w = 8

The width is 8 cm
The length is 8 + 4 = 12 cm

Answer 6

let x be the width
x + 4 is the length

A = width*length

96 = x (x + 4)
96 = x^2 + 4x
x^2 + 4x - 96 = 0

(x + 12) (x - 8) = 0
x = 8 or -12

since distance can't be a negative number. 8 is the answer

width = 8 cm
length = 8+4 = 12cm

Answer 7

l=length w= width

first make it so that only one variable is there

l=w +4
w=w

put it it the equation and simplify

w X w+4 = 96

w²+4w=96

w²+4w-96=0

then factor

(w-8)(w+12)

w-8=0 w+12=0
w=8 w=-12

because you can't have a negative measurement you choose the positve one (8)

w=8

remember in the beginning?
l=w+4
l=(8)+4
l=12


as you can see it works

8X12=96

and the length is 4 cm longer than it is wide

Answer 8

h x w=96
h = w + 4
(w + 4) x w = 96
w^2 +4w -96 = 0
(w + 12) x (w - 8) = 0
w = 8
h = 12

Answer 9

L=4+W
LxW=96
W=96/L
L=4+96/L
L^2=4L+96
L^2-4L-96=0

Solve for L & W.

Answer 10

Length and width of what ?