The area of a rectangle is 2 square feet. the perimeter of the rectangle is 9 ft. find the length, l , and width, w , of the rectangle. what is l squared plus w squared ?

To solve this question:

We apply rectangle concepts.We build a system for the equations of the length and width, and find them solving a quadratic equation.

Doing this, we get that:

The length is of 4 feet, the width is of 0.5 feet, and length squared plus width squared is 16.25.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

.

This polynomial has roots such that , given by the following formulas:

Rectangle:

A rectangle has two dimensions, length l and width w.

It's area is given by:

It's perimeter is given by:

The area of a rectangle is 2 square feet.

This means that , and thus:

The perimeter of the rectangle is 9 ft.

This means that:

Since

Applying cross multiplication:

Solving the quadratic equation, we find the value of the dimensions.

It is a quadratic equation with . So

Thus, a possible answer is given by:

Length of 4 feet, width of 0.5 feet:

A similar question is given at link

Your problem conditions give rise to two equations in l and w.
   area = 2 ft² = lw
   perimeter = 9 ft = 2(l+w)

For l and w in feet, we can substitute for l in the first equation using
   9/2 - w = l . . . . . . .from the second equation
   2 = (9/2 -w)w . . . . substituting for l in the first equation
   w² -9/2w +2 = 0
   (w - 1/2)(w - 4) = 0
   w = 1/2 or 4
   l = 9/2-w = 4 or 1/2

The length and width of the rectangle are 4 ft and 1/2 ft.

l² + w² = (4 ft)² + (1/2 ft)²
l² + w² = 16.25 ft²

Reflection across the x-axis and then a translation.

Step-by-step explanation: