Question

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

Answer 1

Answer:

12 inches

Step-by-step 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

Answer:

Length of Shortest Side = 12 inches

Step-by-step 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