Solving a Quadratic Geometry Problem (2.7.2)

Question 1

• Process for solving word problems:
• Define the variable.
• Write what facts you know.
• Create the equation.
• Solve the equation.
• Check your answer.

Answer 1

• Process for solving word problems:
• Define the variable.
• Write what facts you know.
• Create the equation.
• Solve the equation.
• Check your answer.

Question 2

• Geometry problems generally use at least one of the many formulas everyone knows for area, surface area, circumference, volume, etc. They help you set up your equations.

Answer 2

• Geometry problems generally use at least one of the many formulas everyone knows for area, surface area, circumference, volume, etc. They help you set up your equations.

Question 3

In reading this problem, you find several facts and know that you are being asked to find the dimensions of the room; i.e., its length and width.

Answer 3

In reading this problem, you find several facts and know that you are being asked to find the dimensions of the room; i.e., its length and width.

Question 4

Now you can define your variables and set up the equation for the perimeter.

You can even simplify the equation by noticing that 2 factors out of everything.

Answer 4

Now you can define your variables and set up the equation for the perimeter.

You can even simplify the equation by noticing that 2 factors out of everything.

Question 5

You can also set up an equation for the area of the room.
Knowing this gives you two equations.

Now, solve one equation for w, in terms of L. Substitute that into the other equation and solve for L.

In solving this equation, you will find two values for L, 5 and 12.

By substituting these back into w = 17 – L, you can determine the actual values for the length and width of the room.

Answer 5

You can also set up an equation for the area of the room.
Knowing this gives you two equations.

Now, solve one equation for w, in terms of L. Substitute that into the other equation and solve for L.

In solving this equation, you will find two values for L, 5 and 12.

By substituting these back into w = 17 – L, you can determine the actual values for the length and width of the room.