Question

Follow instructions on the photo [Edited]: Set up an equation and solve the problem The perimeter of a rectangle is 52 inches, and it’s area is 144 square inches. Find the length and width of the rectangle I need the smaller value and larger value

Answer 1

Hello!

First, let's remember some properties about the rectangle:

• Perimeter,: sum of all four sides.

,

• Area,: length * width.

Now, let's imagine a rectangle that we don't know the measurements of the sides. We can call them X and Y.

Now, let's write an equation for the perimeter of this rectangle:

P = x +x +y +y

P = 2x +2y

2x + 2y = 52

Now, let's write an equation for the area of the same rectangle:

A = x * y

x * y = 144

At this moment, we have two equations that have the same value for X and Y. So, we can create a system and solve it, look:

If we solve the second equation using the Bhaskara Theorem, we'll obtain two solutions:

y' = 8

y" = 18

We will use the first solution (y=8) as the value of y, and replace it in the equation i:

Now, let's use the second solution (y=18) as the value of y, doing the same way:

So, in this exercise we have two possible solutions for the system, look:

1st: (8,18)

2nd: (18,8)