Translate the following into a quadratic equation, and solve it:?

Question

The lenth of a rectangular garden is three times its width; if the area of the garden is 75 square meters, what are its demensions?

Answer 1

L = 3 w
Area = LW = 75
from equation 1

3W *W = 75
3W² = 75
W² = 75 / 3
w² = 25
w = √25
W = ± 5
where there is no negative length
so
width = 5 m
Length = 3*5 = 15 m

Answer 2

A=wl=75 where w is width and l length
l=3w

A=3w^2=75
w^2=75/3=25
w = 5 meter

Answer 3

Take x to be its width and y to be its length. Write the equations as follows:

3x = y
xy = 75

Now, substitute 3x in for y in the second equation:

x(3x) = 75

Solve:

3x^2 = 75
x^2 = 25
x = +/- 5

Since the width must be a postive value:

x = 5

and 3(5) = y

y = 15

Your dimensions are 5 meters by 15 meters

Answer 4

with out utilising formulation, the only way is winding up the sq.... evaluate that: (a+b)^2 = a^2 + 2ab +b^2 The proceeding is: one million) divide each and every so as that a metamorphosis to one million b) divide b by 2 and get the sq. of the effect 3) upload and subtract the fee(sq. of b/2) 4) upload the two final numbers and write the sq.. 5) Then remedy the equation. a) 2x^2 + 8x + 7 = 0 ==> x^2 + 4x + 7/2 = 0 ==> x^2 +4x + 4 - 4 + 7/2 = 0 ==> (x+2)^2 -one million/7 = 0 ==> (x+2)^2 = one million/7 ==> x + 2 = sqrt(one million/7) or x+ 2 = -sqrt(one million/7) Then the roots are x = -2 + sqrt(one million/7) or x = -2 - sqrt(one million/7) ok! b) 3x^2 -4x - 5 = 0 ==> x^2 -(4/3)x -5/3 = 0 ( divide 4/3 by 2, sq. it, upload and subtract) ==> x^2 -(4/3)x + 4/9 - 4/9 - 5/3 ==> x^2 -(4/3)x + 4/9 - 19/9 = 0 ==> x^2 -(4/3)x + 4/9 = 19/9 ==> (x -2/3)^2 = 19/9 ==> the roots are x -2/3 = sqrt(19)/3 ==> x = (2+ sqrt(19) / 3 or x-2/3 = -sqrt(19)/3 ==> x = (2-sqrt(19) / 3 ok! c) 6x^2 -x -12 = 0 (divide by 6) ==> x^2 - (one million/6)x -2 = 0 .... (divide one million/6 by 2, sq., upload and subtract) x^2 - (one million/6)x +one million/a hundred and forty four - one million/a hundred and forty four -2 = 0...( upload the final 2 numbers) x^2 - (one million/6)x + one million/a hundred and forty four - 289/a hundred and forty four = 0 ==> (x- one million/12)^2 = 289/a hundred and forty four Then the roots are: x -one million/12 = 17/12 ==> x = 3/2 or x-one million/2 = -17/12 ==> x = -4/3 ok!

Answer 5

It is easy to solve if you understand the ideology of the statement. Let the width be "x". Now its length will be "3x". NOw the Area will be

Area = 3x X x
= 3x^2.
As Area = 75. so we can write
3x^2. = 75
By solving this we can have.
x = 5
Now the dimensions can be calculated.
as width = 5 meters
Length. = 3x
= 3 X 5
= 15 meter.
I hope this will help.
Regards.

Answer 6

let the width equal x
length is 3 times bigger than the width =3x
area = LxW
3x times x = 75
3x^2 = 75
x^2 = 25
x = 5
sixe of rectangle is 5 x 15 meters

Answer 7

L=3W
Area=75
Area= Length times Width
75=(3W)W
3w^2=75
w^2=25
Square root both sides:
W=5 meters
L=3W
L=15 meters

Answer 8

suppose the length is x and width is y
then x = 3y equ [1]
x* y = 75sq m
substituting x with y we get
3y^=75sq ms
y^ =75/3=25 ms
y=5m
x =3y =5*3=15m
l=15m, w=5m

Answer 9

x=width

area=x*3x

75=3x^2

3x^2-75=0 div by 3

x^2-25=0

(x+5)(x-5)=0

x=5 width, length 3x=3*5=15

15*5=75

Answer 10

L = 3W; LW = 75; 3w^2 = 75; w = 5.