Final answer:
The side lengths of the rectangle are approximately 5.66 inches and 7.07 inches.
Step-by-step explanation:
To find the side lengths of the rectangle, we need to create two equations using the given information. Let's assume the length of the rectangle is 'L' and the width is 'W'. The area of the rectangle is given by the equation L x W = 40 and the perimeter is given by 2L + 2W = 48.
To solve these equations, we can use substitution or elimination method. Let's solve using the substitution method.
From the area equation, we can express one variable in terms of the other, for example, L = 40/W. Next, substitute this value of L in the perimeter equation, which gives us 2(40/W) + 2W = 48.
Simplifying the equation, we get 80/W + 2W = 48. Multiply through by W to eliminate the denominators, which gives us 80 + 2W^2 = 48W. Rearranging the equation, we get 2W^2 - 48W + 80 = 0.
Using the quadratic formula or factoring, we can solve for W and find that W is approximately 5.66 or -2.83. Since the width of a rectangle cannot be negative, we discard the negative value. Therefore, the width of the rectangle is approximately 5.66 inches.
To find the length, we can substitute this value of W into the area equation. L x 5.66 = 40. Solving for L, we get L is approximately 7.07 inches. So the side lengths of the rectangle are approximately 5.66 inches and 7.07 inches.