Question

A rectangular garden has an area of 14 m² and a perimeter of 18 meters find the dimensions of the rectangular garden

Answer 1

$\small \purple {\sf{quєѕtíσn !}}$

A rectangular garden has an area of 14 m² and a perimeter of 18 meters find the dimensions of the rectangular garden.

$\small \blue {\sf{αnѕwєr :- }}$

you can get the answer without using quadratic equations, so first we'll get the answer using arithmetic and then using quadratic equations

38/2=19, half of the perimeter

84=2*2*3*7=(2*2*3)*(7)=12*7 and 12+7=19

length and width are 7 and 12 or 12 and 7 (meters)

P=2l+2w

38=2l+2w

19=l+w

l=19-w

A=lw

84=(19-w)w

84=19w-w2

w2-19w+84=0

factor

now, you factor 84 which is what I did at the top...

84=(2*2*3)*(7)

(w-12)(w-7)=0

w-12=0

w=12 (and l=7)

or,...

w-7=0

w=7 (and l=12)

Answer 2

Answer:

you can get the answer without using quadratic equations, so first we'll get the answer using arithmetic and then using quadratic equations

38/2=19, half of the perimeter

84=2*2*3*7=(2*2*3)*(7)=12*7 and 12+7=19

length and width are 7 and 12 or 12 and 7 (meters)

P=2l+2w

38=2l+2w

19=l+w

l=19-w

A=lw

84=(19-w)w

84=19w-w2

w2-19w+84=0

factor

now, you factor 84 which is what I did at the top...

84=(2*2*3)*(7)

(w-12)(w-7)=0

w-12=0

w=12 (and l=7)

or,...

w-7=0

w=7 (and l=12)