Lesson Worksheet: Applications of Quadratic Equations Mathematics • 9th Grade

In this worksheet, we will practice solving word problems by forming and solving quadratic equations.

Q1:

The diagram shows a rectangular prism, where the area of its net is 580. Find the value of 𝑥.

Q2:

What is the perimeter of a rectangle whose length is 7 cm more than its width and whose area is 78 cm2?

Q3:

Determine the positive number whose square exceeds twice its value by 15.

Q4:

Find the positive number which is 66 less than twice its square.

Q5:

The difference between the lengths of the diagonals of a rhombus is 5 cm. Given that its perimeter is 304 cm, find the lengths of the diagonals to the nearest cm.

  • A115 cm, 100 cm
  • B219 cm, 209 cm
  • C204 cm, 204 cm
  • D110 cm, 105 cm

Q6:

Point 𝐾 lies between points 𝐽 and 𝐿. If 𝐽𝐾=𝑥+8𝑥, 𝐾𝐿=3𝑥2, and 𝐽𝐿=40, find the length of 𝐽𝐾.

Q7:

The diagram shows a trapezoid and a rectangle.

Write an expression for the area of the rectangle.

  • A(2𝑥+1)(𝑥9)
  • B2(2𝑥+1)(𝑥9)
  • C(2𝑥1)(𝑥+8)
  • D(2𝑥+3)(𝑥7)
  • E2((2𝑥+1)+(𝑥9))

Write an expression for the area of the trapezoid.

  • A(𝑥7)(𝑥+3)
  • B(𝑥+6)(𝑥7)
  • C(𝑥8)(𝑥+7)
  • D(𝑥3)(𝑥6)
  • E(𝑥+5)(2𝑥3)

If the trapezoid and the rectangle have the same area, find the value of 𝑥 using a suitable equation.

Q8:

The sum of the squares of two positive real numbers is 542. Given that one of them is 18, find the value of the other one.

  • A866
  • B866 or 866
  • C2131
  • D218
  • E218 or 218

Q9:

A right triangle has sides of lengths 𝑛 cm, 3(𝑛+1) cm, and (3𝑛+4) cm. Find the length of its shortest side.

Hint: first, decide which side is the hypotenuse.

Q10:

If the area of the given figure is 138 cm2, what is the value of 𝑥?

This lesson includes 22 additional questions and 184 additional question variations for subscribers.

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