Question

The area of a rectangular back yard is 55 square meters. The length of the yard is one meter greater than twice the width.

What is the width of the yard in meters?
Provide your answer below:

Answer 1

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

Answer 2

5

Explanation:

Area= 55

width=y(unknown)

length=1+2y(given)

formula for finding A.=l*b

(1+2y)(y)= y+2y^2

y+2y^2=55

2y^2= 55-y

y=5

verification

2*5^2=55-5

2*25=55-5