Use sidewalk chalk and a ruler to draw a rectangle

Question

With an area of 48 square inches (area=length×width) and a perimeter of 38 inches

Answer 1

A rectangle has a length which we will call L, and a width that we will call W.

Area = L*W

Perimeter = L + L + W + W = 2L + 2W

Now replace Area and Perimeter with the numbers given in the problem:

48 = L*W (Equation 1)

38 = 2L + 2W (Equation 2)

Solve Equation 1 for W by dividing both sides of the equation by L:

W = 48/L

Now replace W with 48/L In Equation 2

38 = 2L + 2(48/L)

Now solve for L:

38 = 2L + 96/L

38L = 2L² + 96

2L² - 38L + 96 = 0

L² - 19L + 48 = 0

(L-3)(L-16) = 0

L = 3 or L = 16

Replace L with values in revised Equation 1 to solve for W:

W = 48/L

= 48/3 OR 48/16

= 16 OR 3

So the rectangle will have the sides of 3 in and 16 in