Question

The lemgth of a rectangle is 4 more than 2 times its width. Find the lemgth and width of the rectangle with an area of 160. What is the length and width?

Answer 1

The length of the rectangle = 20

The width of the rectangle = 8

Explanation:

Step(l):-

let 'W' be the width of the rectangle

Given the length of a rectangle is 4 more than 2 times its width

length of a rectangle(L) = 4+2W

Given the Area of rectangle = 160

Step(ii):-

we know that the area of the triangle = length ×width

(4+2w)w= 160

`2w^(2) +4w-160=0`

`2(w^(2) +2w- 80)=0`

`w^(2) +10w-8w- 80=0`

`w(w +10)-8(w+10)=0`

`(w+10)(w-8) =0`

`w+10=0 , w-8=0`

w = -10 and w =8

Step(lll)

we can choose the width is 'w' = 8

now the length of the rectangle = 4+2(8) = 20

The width of the rectangle is '8'

Conclusion:-

The length of the rectangle = 20

The width of the rectangle = 8