Albert's rectangular garden is 6ft by 3ft. He wants to lengthen both dimensions by the same number of feet so that the new area will be 40 square feet. What will be the new dimensions?

8 and 5

Step-by-step explanation:

Let the number of feet added = x

(x + 6) ( x + 3) = 40               Remove the brackets

x^2 + 6x + 3x + 18 = 40        Combine like terms on the left

x^2 + 9x + 18 = 40                Subtract 18 from both sides

               -18    -18

x^2 + 9x = 22                        Subtract 22 from both sides

x^2 + 9x - 22 = 0

This quadratic factors

(x + 11)(x - 2)

x + 11 = 0

x = - 11 which makes not sense.

x - 2 = 0

x = 2

The answer is x = 2

Check

6+2 = 8

3+2 = 5

8 * 5 = 4- just as it should.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3