Math Question?

Question

The length of a garden is 9ft longer than the width. If the area of the garden is 70 sq ft. What are the dimensions?

Any explanations

Answer 1

l = 9 + w
A = lw
70 = (9 + w)w
70 = 9w + w^2
w^2 + 9w - 70 = 0
(w + 14)(w - 5) = 0
w = 5, -14
But throw out the -14 since length will not be negative. So,

length = 14
width = 5

Answer 2

Let x equal the length, so then the width would equal x + 9.

x(x+9)=70
xsquared + 9x=70
so xsquared +9x - 70 =0

when you factorise the quadratic you get (x + 14)(x - 5) = 0
so x is 5 or -14
obviously 5 is the answer because you can't have a negative measurement.

so the width is 5 and the length is 5+9 which is 14

Answer 3

Let the width =x ft
so the length=(x+9) ft
area =LXW=x(x+9)=70 sq ft
or x^2+9x-70=0
or x^2-5x+14x-70=0
or x(x-5)+14(x-5)=0
or (x-5)(x+14)=0
so x=5 or x=-14(rejecting the -ve value as length can never be -ve)
so Width =5ft & Length=5+9=14 ft ans

Answer 4

Area=Length X Width
We know Area=70
Let width be x
Therefore length=x+9
70=x(x+9)
70=x^2+9x
x^2+9x-70=0
(x+14)(x-5)=0
For (x+14)(x-5) to multiply out to zero, at least one of the factors must be zero.
If x+14=0, x= -14
If x-5=0, x=5. Therefore length =5+9 =14
Dimensions are 5 and 14

Answer 5

70 = 1 2 5 7 10 14
I don't know how you do the working out but the length must 14ft and the width 5ft

Answer 6

Let x = length

Find the length
x * (x - 9) = 70
x^2 - 9x = 70
x = 14

Find the width:
= 14 - 9
= 5

Answer: length = 14 ft, width = 5 ft

Proof:
= 14 * 5
= 70

Answer 7

Area formula

A = L x W

70 = (w + 9)w

The distributive property on the right side of the eqution.

70 = w² = 9w

Transpose 70

70 - 70 = w² + 9w - 70

0 = w² + 9w - 70

0 = w² + 14w - 5w - 70

Group factor

0 = (w² + 14w - (5w - 70)

0 = w(w + 14) - 5(w + 14)

0 = (w - 5)(w + 14)

- - - - - -

Roots

w - 5 = 0

Transpose 5

w - 5 + 5 = 0 + 5

w = 5

- - - - - -

w + 14 = 0

Transpose 14

w + 14 - 14 = 0 - 14

w = - 14. . .←. .not used

- - - - - - - - -

The width is 5 feet

The length is w + 9

5 + 9 = 14

The length is 14 feet

- - - - - - - -s-

Answer 8

if we assign the width as 'x' ft then the length will be 'x+9'
thus giving us an equation with the variable 'x'.

(x)*(x+9)=70
which will give us : x=5 and x=-14
since length or width cannot be a negative value so we will only take x=5.
therefore length=14
width=5.

Answer 9

let l and w be the length and width respectively.
area=lw=(w+9)w=70
w^2+9w-70=0
ax^2+bx+c=0
a=1 b=9 c=-70
x=[-b+-sqrt(b^2-4ac)]/2a
solving w=5 or -14
5 is positive and the width
so, the length is 5+9=14
check: area=5(14)=70

Answer 10

L(L-9) = 70
L^2 - 9L - 70 = 0
(L-14)(L+5) = 0
L = 14 ft, the length
L-9 = 5 ft, the width