a little math?

Question

the length of a rectangular frame is 5cm more than the width. The area inside the frame is 84 square cm..FIND THE WIDTH OF THE FRAME :)

wna make sure my answer is right..
thnks

Answer 1

Let W be the width.
Let W+5 be the length.

Area = width x length.

W(W+5) = 84
W² + 5W = 84
W² + 5W - 84 = 0
(W - 7)(W + 12) = 0

The width is either 7 cm or -12 cm. Only one of these is reasonable. :-)

Double-check.
7cm x 12cm = 84cm

The width is 7 cm.

Answer 2

Let the width of the rectangle be x.

Hence, the area inside the frame is

A = x(x+5) = 84
x^2 + 5x = 84
x^2 + 5x - 84 = 0
(x+12)(x-7) = 0
x = -12 or x = 7
Since x >= 0,
x = 7

hence, the width of the rectangular frame is 7cm.

Answer 3

I am not 100% sure this is correct because my memory isn't too good.
So say the width is x-5, therefore
length=x

And we know the area of a rectangle is
l*w,
so
84=x(x-5)
x^2-5x-84=0
(x+7)(x-12)

therefore x=-7 , x=12. Reject the -7 because you can't have a negative width or length.
recall width= x-5
width=12-5
=7

Answer 4

x = width
x + 5 = length

Area = width * length

84 = x (x + 5)
84 = x^2 + 5x
0 = x^2 + 5x - 84

use quadratic fomrula and you'll get x = 7

so width: 7 cm
length: 12 cm

Answer 5

x= width
x+5=length

x(x+5)=84
x^2+5x=84
x^2+5x-84=0
x=7
x+5=12

The width is 7cm while the length is 12 cm.