Question

1. What is the length of the shortest side if the perimeter of the rectangle is

56 inches?
3х
5х – 4

Answer 1

12 inches

Explanation:

The length is the longest side.

The width is the shortest side.

Length :
`l=5x-4`

Width :
`w=3x`

Apply formula for the perimeter of a rectangle.

`P=2l+2w`

`P=perimeter\\l=length\\w=width`

Plug in the values.

`56=2(5x-4)+2(3x)`

`56=10x-8+6x`

`56=16x-8`

`64=16x`

`4=x`

The shortest side is the width.

`w=3x`

Plug in the value for x.

`w=3(4)`

`w=12`

Answer 2

Length of Shortest Side = 12 inches

Explanation:

Length of Shortest Side = L = 3x

Length of Longest Side = W = 5x-4

Condition:

2L+2W = Perimeter

2(3x)+2(5x-4) = 56

6x+10x-8 = 56

16x-8 = 56

Adding 8 to both sides

16x = 56+8

16x = 64

Dividing both sides by 14

=> x = 4

Now,

Length of the Shortest Side = L = 3(4) = 12 inches

Length of the Longest Side = W = 5(4)-4 = 16 inches