Forming Quadratic Equations GET

The width of a classroom is 2m less than the length, and the area is 180m². Identify the correct equation.

• x² - 2 = 180

• x(x - 2) = 180

• x(x - 2) + 180 = 0

• x² - 2x = 0

A girl is 3 years younger than her brother. The product of their ages is 238. If her brother's age is x, then identify the correct equation.

• x - 3 * x = 238

• x² - 3x + 238 = 0

• x² + 3x + 238 = 0

• x (x - 3) = 238

The perimeter of a rectangular classroom is 46m and it's area is 130m². Choose the correct pair of equations which describe the situation.

• xy = 130 and x + y = 46

• xy = 130 and 2x + 2y = 46

• xy = 46 and x + y = 130

• x² + y = 156

Two square rooms have a total floor area of 230m². One is 4m bigger each way than the other. Let x be the size of the length of the smaller room. Set up an equation to describe the situation.

• (x - 4)² + (x + 4)² = 230

• 2(x + 4)² = 230

• x ( x + 4 ) = 230

• x² + (x + 4)² = 230

When the numbers 10 and 19 are both increased by the same amount, the product of the new numbers is 360. Describe the situation algebraically.

• (10 + x) (19 + x) = 360

• 10 + 19 + 2x = 360

• 10 x 19 = 360

• (x + 10) (x + 19) = 0

A man is 39 years old and his daughter is 11 years old, how many years ago was the product of their ages 128? Set up an equation to illustrate this algebraically.

• x² + 50x + 128 = 0

• (x - 39) (x - 11) = 128

• 39 x 11 = 128

• (39 - x) (11 - x) = 128

The length of a rectangle is xcm and the width is 3cm less. The area is 10cm². Which equation describes this situation?

• x ( x + 3) = 10

• x² - 3x = 10

• x² - 6 = 10

• x ( x - 3) + 10 = 0

The area of a square of side length (x + 2)cm is 25cm². Express this algebraically.

• x² + 4 = 625

• x(x + 2) = 25

• x² + 4 = 25

• (x + 2)² = 25

The two shorter side lengths of a right-angled triangle are xcm and (x+1)cm, the longest length (hypotenuse) is 5cm. Express this situation algebraically.

• x² + x = 5

• x (x + 1) = 5

• x (x + 1) = 25

• x² + (x + 1)² = 25

1 more than the square of x is 50. Choose the equation which satisfies this relationship.

• x² + 1 = 49

• x² + 1 = 50

• x (x + 1) = 50

• (-7) x (-7) + 1 = 50