MaTH HELP!!!!???

Question

helps me on this problem:

The length of a rectangle is 4 cm more than the width. The area is 97 cm ^2. Find the length and the width.

please show all steps! cause i cant get an answer fot this! thanks :D

Answer 1

are you sure the area is 97? i think it's 96

area of rectangle = length * width
let x : width
x + 4 : length
x * (x + 4) = 96
x^2 + 4x = 96
x^2 + 4x - 96 = 0
through factoring or the quadratic equation:
(x + 12) (x - 8) = 0

then
x + 12 = 0 or x - 8 = 0
if x + 12 = 0 then x = -12 since width cannot be negative this is not the answer
so x - 8 = 0 then x = 8 so the width is 8 cm and the length is 12 cm
12 cm * 8 cm = 96 sqcm

hope this helps. if 97 is the correct area, you can still get the length and width via the quadratic equation but don't expect whole numbers. good luck.

Answer 2

so...
draw a pic of a rectangle. one side is x (width) and the other side is x+4 (length).
area of a rectangle = length times width
so... x*(x+4)=97
then solve...x^2+4x=97
x^2+4x-97=0
then quadratic formula...x=(-4plus or minus square root of (4^2-4*1*-97))/2
and solve it...x=(-4plus or minus square root of (8+388))/2
x=(-4+(square root of 396))/2
x=(-4-(square root of 396))/2
so then, since the second one doesnt work, x=the first one
and then you plug it into the pic you made first, and everyone is happy

Answer 3

the length is 4 area is 97square cm. is this volume or area? there is no width if it is area. here is the problem for area:

L x W= area
4 x W= 97
divide by 4 both sides
w=24.25.

if it is for volume, the equation goes like this:

LxWxH= Volume
4xLxW=97
divde by 4
LxW=24.25
and then................
i think this is a area question, not volume, so i cant get that one any further! but this should help.

Answer 4

let x= length and y=width

x=y+4

x*y=97

x(x+4)=97

x^2+4x=97

x^2+4x-97=0