Question

The length of a rectangular shaped park is (3x+5) miles. The width is (2x+8) miles. The area of the park is 360 square miles. What are the dimensions of the park?

Answer 1

Area=legnth times width
(3x+5)(2x+8)=360
first expand

6x²+34x+40=360
minus 360 both sides
6x²+34x-320=0
factor out 2
2(3x²+17x-160)=0
factor inner by trial and error
(2)(x-5)(3x+32)=0
set to zero
x-5=0
x=5

3x+32=0
3x=-32
x=-32/3
false, a dimention can't be negative

x=5

(3x+5)
(3(5)+5)
(15+5)
20
length is 20miiles

(2x+8)
(2(5)+8)
(10+8)
18
width is 18 miles


it is 20 miles by 18 miles