Question

The area of a rectangular wall of a barn is 64 square feet. Its length is 8 feet longer than twice its width. Find the length and width of the wall of the barn.

Answer 1

Answer:

Length =  16 feet , width = 4 feet .

Step-by-step explanation:

Given  : The area of a rectangular wall of a barn is 64 square feet. Its length is 8 feet longer than twice its width.

To find : Find the length and width of the wall of the barn.

Solution : We have given

Area of rectangle = 64 square feet.

According to question :

Let width = W.

Length is 8 feet longer than twicw its width .

Length = 2W + 8

L = 2W + 8.

Area of rectangle = length  * width.

Plug the values.

64 = (2W +8 )W .

64 = 2W² + 8W.

On subtracting both sides by 64.

2W² + 8W- 64 = 0

On taking 2 common from all.

W² + 4 W- 32 = 0

On factoring

W² + 8W -4W - 32 = 0

W (W +8) -4 ( W + 8) = 0

On grouping

(W+8)( W -4) = 0

W = -8 feet, W = 4 feet. ( ignore negative value)

Width = 4 feet.

Length = 2 (4)+ 8.

Length = 16 feet.

Therefore, Length =  16 feet , width = 4 feet .

Answer 2

L×w=64 ft^2...(1)
2w+8= l...(2)

l=64-w...(1a)

2w+8= 64-w
2w+w+8=64
3w=64-8
3w÷3= 56÷3
w=18.6'

l×w= 64
l×18.6= 64
l= 64÷18.6
l= 3.44 to the nearest hundredths.