Solving Quadratic Word Problems: Finding the Dimensions of a Rectangle

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In summary, the original rectangle has dimensions of 4mm and 15mm, and the length and width were increased by 5 millimetres each. This resulted in an area of 180 square millimetres. By setting up the equation (x + 5)(y + 5) = 180 and plugging in the given area of 60 square millimetres, the dimensions of the original rectangle can be easily found.
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leekiss
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A rectangle has an area of 60 square millimetres. If the length and width were each increased by 5 millimetres, the area would be 180 square millimetres. Find the dimensions of the original rectangle.

Could someone please help me! I have tried everything.

The answers are 4mm and 15mm.
 
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  • #2
Let the length be x mm, and the width be y mm. What can you say about x and y? What can you say about x+5 and y+5?
 
  • #3
(x + 5) x (y + 5) = 180

Expanding,
xy + 5x + 5y + 25 = 180

The value of xy is given in the question. Plug in into the equation above. The rest should be easy.
 

What are "Quadratic word problems"?

Quadratic word problems are mathematical problems that involve finding the solutions to quadratic equations in the form of ax^2 + bx + c = 0. These problems are called word problems because they are presented in the form of a real-world scenario or situation.

How do I solve Quadratic word problems?

To solve Quadratic word problems, you need to follow these steps:

  • Read the problem carefully and identify the given information and what you need to find.
  • Write a quadratic equation based on the given information.
  • Solve the equation using factoring, the quadratic formula, or completing the square.
  • Check your solution by plugging it back into the original equation.

What are the common types of Quadratic word problems?

The common types of Quadratic word problems are:

  • Maximization and minimization problems
  • Motion problems
  • Area and perimeter problems
  • Revenue and profit problems
  • Projectile motion problems

What are some tips for solving Quadratic word problems?

Here are some tips for solving Quadratic word problems:

  • Read the problem carefully and identify the given information and what you need to find.
  • Draw a diagram or visualize the problem to help you understand it better.
  • Choose a variable to represent the unknown quantity.
  • Write a quadratic equation based on the given information and the variable you chose.
  • Use appropriate methods such as factoring, the quadratic formula, or completing the square to solve the equation.
  • Check your solution by plugging it back into the original equation.

What are some real-life applications of Quadratic word problems?

Quadratic word problems have various real-life applications, such as:

  • Calculating the maximum or minimum value of a product to maximize profit or minimize cost
  • Determining the trajectory of a projectile, such as a ball thrown in the air
  • Finding the dimensions of a rectangular or square field with a given area
  • Calculating the time it takes for an object to reach a certain height when thrown into the air
  • Estimating the speed of a moving object based on its distance and time traveled

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