Sam is going to plant a rectangular flower garden next to his house. There will be a fence on three sides of the garden (fencing is not necessary along the house). The area of the garden is to be 1,000 sq. ft., and he has 90 feet of fencing available. Determine the dimensions of the garden. There are 2 solutions. One is 25 ft., 40 ft.

Determine the other solution: width ft., length ft.

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Let dimensions of the field be l abd b.

since darden is rectangular so

Area= l x b (i)

By given condition

l x b= 1000 sq ft (ii)

since one side is house ,so fencing required three side only.

Thus

2b+l= 90 (iii)

l=90-2b (iv)

substitute l from (iv0 in (ii) ,we have

(90-2b) x b=1000

45b-b^2=500

b^2-45b+500=0

b^2-20b-25b+500=0

(b-25)(b-20)=0

Thus

b=25 or 20 ft

**so other diemensions are**

**b=25 then l =20 ft**

**b=20 then l= 25 ft**

The previous answer does indicate the second width required and we must still find the length We have widths 20ft and 25ft (given) so now must find the other length in terms of the width of 20ft.

Substitute into a previous equation:

`2b+l=90` becomes `2(20) +l=90`

`therefore 40+l=90`

`therefore l=50`

**Ans: we have second set of dimensions: 20ft and 50ft**

**Sources:**

Sorry for last two lines were not correct.

correction in answer

If b= 25 ft then l= 40 ft it is given.

If b= 20 then l= (1000/20)= 50 ft

Thus other solution is

**b=20 ft and length= 50 ft. **

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