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?

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

Answer Link

sheenuvt12 sheenuvt12 · Answer 2 · 2022-05-24T06:48:44+02:00

The dimensions of the park are length=20 mile and breadth= 18 miles

What is Area of rectangle?

Area of rectangle is the product of its length and its breadth

Given: length= (3x+5) miles and breadth = (2x+8)

Area of rectangle = 360 sq. miles

l * b = 360

(3x+5)(2x+8) =360

6x² +24x+ 10x + 40= 360

6x² +34x + 40 =360

6x²+34x-320=0

3x²+17x-160=0

(3x+2)(x-5)=0

x= -32/5 or x= 5

Thus, length= 3x+5 =20 miles

breadth= 2x+8= 18 miles

Learn more area of rectangle here:

https://brainly.com/question/20693059

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