Brian P. answered • 09/27/20
Experienced Tutor Specializing in Math and Computer Skills
First, identify what you have been given, and what you need to find. You have two different pieces of information about the rectangle: how the sides compare, and also the area. You need to find the measurements of the two sides.
Next, figure out how to write the equations for the two pieces of information you've been given:
* The length is 5 inches more than two times the width. Let's use the variables L and W for the length and width. So, we can write this equation like this: L = 2 W + 5
* The area is 33 square inches. The formula for the area of a rectangle is A = L * W, so we can write this one 33 = L * W.
Third step: solve one of the equations for ONE of the variables. One of our equations is already written like that: L = 2 W + 5 . You can see that it is already solved for L. If it weren't written like that, you would need to choose one of the equations to solve for either one of the variables.
Fourth step: substitute the equation that's solved for one variable INTO the other equation. Since the first equation tells us that L equals 2 W + 5, then wherever we see "L" in the second equation, we can substitute 2 W + 5. USE PARENTHESES around the expression that you put in, so that you don't do it wrong. Here's how we do it:
33 = (L) * W
33 = (2 W + 5) * W
Now solve for W. I'm leaving out explanations because each step uses concepts from Algebra 1 (not Algebra 2):
33 = (2 W + 5) * W
33 = 2 W2 + 5 W
2 W2 + 5 W - 33 = 0
Factor this into:
(2 W + 11)(W - 3) = 0
Set each of the two parts equal to zero, and solve each one. I've split them here into (a) and (b).
(a) (2 W + 11) = 0
2 W = -11
W = -11/2
(b) (W - 3) = 0
W = 3
The two possible answers are W = -11/2 or W = 3. Whenever solving equations for a real-world problem, ask yourself if the answers make sense. Can a rectangle have a negative width of -11/2? No. So we can throw away that answer, leaving W = 3.
Almost done! Look back at the answer to determine what they asked for: "Find the length and the width." We have the width: W = 3. You can calculate the length because you used an equation that was solved for L: L = 2 * W + 5. Substitute 3 in for the W:
L = 2 * (W) + 5
L = 2 * 3 + 5
L = 6 + 5 = 11
It looks like the length is 11. Last step: check the original problem to make sure these answers work! "The length of the rectangle (11) is 5 inches more than 2 times the width (3)": YES. "The area is 33 square inches": 3 x 11 = 33. So the answer is correct! Length is 11, width is 3.
Bridget G.
Thank you so much that explanation was so very helpful!!09/27/20