The area of a rectangle is 72 square inches and the perimeter is 44 inches. Find its dimensions.
area=lw
lw=72 or l=72/w
P=2(l+w)=2(72/w + w)
44=2(72/w+w)
22w=7+w^2
w^2-22w+72=0
(w-18)(w-4)=0
so w is 18, or 4, and you can solve for the length from l=72/w
To find the dimensions of the rectangle, we need to set up a system of equations based on the given information. Let's denote the length of the rectangle as "l" and the width as "w".
We know that the area of a rectangle is given by the formula A = l * w, and in this case, the area is 72 square inches. So, our first equation is:
l * w = 72 ---- (Equation 1)
We also know that the perimeter of a rectangle can be calculated using the formula P = 2 * (l + w), and in this case, the perimeter is 44 inches. So, our second equation is:
2 * (l + w) = 44 ---- (Equation 2)
Now, we can solve this system of equations to find the values of "l" and "w".
Let's rearrange Equation 2 to solve for either "l" or "w". Dividing both sides of the equation by 2 gives us:
l + w = 22
Now, we can solve this equation for "l" in terms of "w" by subtracting "w" from both sides:
l = 22 - w
Now, substitute this expression for "l" into Equation 1:
(22 - w) * w = 72
Expand the equation:
22w - w^2 = 72
Rearrange the equation to bring all terms to one side:
w^2 - 22w + 72 = 0
Now, we have a quadratic equation in terms of "w". We can solve this either by factoring or using the quadratic formula.
Let's use factoring:
(w - 18)(w - 4) = 0
This gives us two possible values for "w": w = 18 or w = 4.
If w = 18, substitute this into our expression for "l":
l = 22 - w = 22 - 18 = 4
If w = 4, substitute this into our expression for "l":
l = 22 - w = 22 - 4 = 18
So, the dimensions of the rectangle are either 4 inches by 18 inches or 18 inches by 4 inches.