Chapter 5

Front

What is the difference of two positive numbers if their sum is 22 and their difference is 12?

Back

The two numbers are 17 and 5.

Front

If the sum of the squares of two numbers is 314, what can we infer about their individual values?

Back

The two numbers can be found using the equations derived from their sum and difference.

Front

What is the formula for the area of a rectangle?

Back

Area = length × width.

Front

How do you find the width of a path around a garden if the area of the path is known?

Back

Set up an equation using the area of the larger rectangle (garden + path) and subtract the area of the garden.

Front

What is the relationship between the sum and difference of two numbers?

Back

If you know the sum (S) and difference (D) of two numbers, you can find the numbers using: x = (S + D)/2 and y = (S - D)/2.

Front

What is the significance of solving quadratic equations in real-life applications?

Back

Quadratic equations can model various real-world situations, such as projectile motion and area problems.

Front

What is a uniform width in the context of geometry?

Back

A uniform width means that the width is the same all around the object, such as a path around a garden.

Front

How do you calculate the area of a path surrounding a rectangular garden?

Back

Area of path = Area of larger rectangle - Area of garden.

Front

What is the Pythagorean theorem?

Back

In a right triangle, a² + b² = c², where c is the hypotenuse.

Front

What are the steps to solve a system of equations?

Back

1. Write the equations. 2. Use substitution or elimination. 3. Solve for one variable. 4. Substitute back to find the other variable.