I have a really Confusing Question

Question

Jose needs to enclose a rectaglar section of his yard. The perimeter of the section is 27 feet and the area is 35 square feet. Find the length and width of the section.

- write an equation for the perimeter of the section

- write an equation for the are of the section.

- using thw equations, solve for the length of the section.

Answer 1

Let l is the length and w is the width of the rectangle.

Perimeter of the rectangle, P = 2(l + w ) =27 feet

Area of the rectangle, A = l w = 35 square feet

2(l + w ) =27 feet

l + w = 27/2        ...... (1)

lw = 35

w = 35/l

Substitute w = 35/l  in equation in (1).

l + ( 35/l) = 27/2   

2 ( l ² +35 )  = 27 l

2l ² -27l + 70 =0

2l ² - 20l - 7l + 70 =0

2l  ( l  - 10 ) - 7( l  - 10 ) =0

l  =10 and  l = 7/2

When  l =10

w = 35/10 = 7/2

When  l =7/2

w = 35/(7/2) = 10

l  = 10 and w = 7/2

l  = 7/2 and w = 10