Step-by-step explanation:
Area of a rectangular backyard is given as 55 m²
the length is 1 m greater than the twice the width
=>l=2w+1---(say A)
we know that
Area of a rectangle is always length * width=A=l*w
Divide both sides by w
A/w=l
put this value of l in (A)
A/w=2w+1
multiply both sides by w
A=w(2w+1)
55=2w²+w
subtract 55 from both sides
2w²+w-55=0
2w²-10w+11w-55=0
2w(w-5)+11(w-5)=0
(2w+11)(w-5)=0
(2w+11=0 , w-5=0
2w=-11. , w=5
w=-11/2 m
width can never be a negative integer so we omit -11/2
we will consider w=5m
put this in (A)
l= 2(5)+1
l=10+1
l=11m
checking ,
A=lw
A=(11m)(5m)
A=55m²
