Question

A rectangle has an area of 56 square inches and a perimeter of 36 inches.

Complete the table and write a system of equations to represent the length and width of the rectangle.

Answer 1

Table #1:

Length (L) | Width (W) | Area (56)

Table #2:

Length (2L) | Width (2W) | Perimeter (36)

Equation #1: L · W = 56

Equation #2: 2L + 2W = 36

Explanation:

Answer 2

Table #1:

Length (L) | Width (W) | Area (56)

Table #2:

Length (2L) | Width (2W) | Perimeter (36)

Equation #1: L · W = 56

Equation #2: 2L + 2W = 36

Explanation:

The following are the formulas used to find the area and the perimeter of a rectangle:

Area = L · W

Perimeter = L + L + W + W

If you group common variables, you can simplify the formula used to find the perimeter down to:

Perimeter = L + L + W + W

Perimeter = 2L + 2W (Since you're adding 2 of each)

Using these formulas, we can insert our values into them. We know that the rectangle has an area of 56 square inches meaning:

L · W = 56

We know that the rectangle has a perimeter of 36 inches meaning:

2L + 2W = 36