Question

The length of a picture frame is 8 inches more than the width. For what values of x is the perimeter of the picture frame greater than 152 inches.

Answer 1

For, "x" greater than 34, the perimeter of the picture frame greater than 152 inches

Solution:

Let "x" be the width of the frame

Given that, The length of a picture frame is 8 inches more than the width

Therefore,

Length = width + 8

Length = x + 8

The perimeter of rectangle is given by formula:

Perimeter = 2(length + width)

Substituting the values we get,

Perimeter = 2(x + 8 + x)

Perimeter = 2(2x + 8)

Perimeter = 4x + 16

The perimeter of the picture frame greater than 152 inches

Perimeter > 152

$4x + 16>152\\\\\text{Subtract 16 from both sides of inequality}\\\\4x + 16 - 16 > 152 - 16\\\\4x>136\\\\\text{Divide both sides by 4}\\\\x>34$

Therefore, for, "x" greater than 34, the perimeter of the picture frame greater than 152 inches