Help with this math problem?

Question

Okay..Please help...

Matt's rectangular patio measures 9 fett by 12 feet.He wants to increase the patio's dimensions so its area will be twice the area it is now. He plans to increase both the length and the width by the same amount ,x. Find x, to the nearest hundredth of a foot..

How would I go about doing this..Please help..I appreciate the help..

Answer 1

Area now = 9*12 = 108 ft^2
New area is 2*108 = 216 ft^2
So (9+x)(12+x) = 216
108 +21x +x^2 = 216
x^2 +21x -108 = 0
x = [ -21 +/- 29.55)/2
x = (-21+29.55)/2 = 4.27 ft

Answer 2

The original dimensions are 9 x 12 ft

let the increase in L and W be x ft

so the dimensions after increase = (9+x) and (12+x) ft

New area = (9+x)(12+x)

It is given that new area is double the original area

so (9+x)(12+x) = 2(9*12) = 216

x^2 + 21x + 108 = 216

x^2 + 21x - 108 = 0

using quadratic formula

x = [-21 + sqrt(441 + 432)] / 2 (ignoring negative value)

x = [-21 + sqrt(873)] / 2

x =( -21 + 29.55) / 2

x = 8.55/2 = 4.28 ft

Answer 3

the original Area of patio is A = x*y = 9*12= 108 ft^2

he wants Area of patio is double so new area is 108*2 = 216 ft^2

and he plans to increase original length and width by them same amount x to get twice original area

therefore the new express formula or area is

A = (9+x)*(12+x) = 216

foil it out
108+9x+12x+x^2 = 216
108+21x+x^2 = 216
x^2+21x-108 = 0
x = 3(√(97)-7)/2 or x = -3(√(97)+7)/2
solve that you will get x = 4.27 ft

Answer 4

New length = 9+x
New width = 12+x
New area = 9*12*2 = 216
So
(9+x)(12+x) = 216
x² + 21x - 108 = 0
x = ½(-21 + √441+432) = ½(-21 + √873) = 4.27 ft.(approx).
Note that we rejected the other root because it
would give a negative value of x.

Answer 5

To solve I used the function (9+x)(12+x)=216.
Basically the current dimensions adding on x equals the new area.
So
(9+x)(12+x)=216
X^2+21X+108=216
X^2+21X-108=0
Using the quadratic formula.... or my graphing calc because I'm lazy your answer is increase both dimensions by 4.27 ft.

Answer 6

First, find the total area currently (9 * 12 = 108)

Then, double it (108 * 2 = 216)

Then, find out what the dimensions need to be
( (x+9)*(x+12) = 216) )

Simplify the equation and solve for x!

Answer 7

(x+9)(x+12) = 2*9*12
x^2 + 21x + 108 = 216
x^2 + 21x - 108 = 0
then use the quadratic equation which yields:

x = (3sqrt(97) - 21)/2 which is about 4.27 feet

Answer 8

currently the area measures 108 feet. therefore the new area measures 216 feet the equation will go like this

(9+x)(12+x)=216 which will become in quadratic form

x^2+21x-108=0

to solve this you will need to use the quadratic equation.